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These were checked for factors under 2^32 and came back negative. Can someone else run the LLR tests on these Proth numbers? I've tried and my LLR program glitches out around bit 131072.
29×2^21019467+1
51×2^21019467+1
If prime, these numbers could land in 11th and 12th in the list of largest known primes. |
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 Crun-chi Volunteer tester
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These were checked for factors under 2^32 and came back negative. Can someone else run the LLR tests on these Proth numbers? I've tried and my LLR program glitches out around bit 131072.
29×2^21019467+1
51×2^21019467+1
If prime, these numbers could land in 11th and 12th in the list of largest known primes.
Those PRP will verify for many days even on fastest CPU on the world.
But Prime95 can be used here, and used all cores in parallel working should get your PRP result pretty fast.
Good luck
____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
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JimBHonorary cruncher
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These were checked for factors under 2^32 and came back negative. Can someone else run the LLR tests on these Proth numbers? I've tried and my LLR program glitches out around bit 131072.
29×2^21019467+1
51×2^21019467+1
If prime, these numbers could land in 11th and 12th in the list of largest known primes.
They're not PRP. They're not realistically going to be prime. You tested for factors under 2^32, i.e. 4,294,967,296 (4.2G). That's really small. We sieved SoB/PSP/ESP to 103,741,790,000,000,000 (103.7P) or about 25 million times as high. Primes are vanishingly rare for candidates that large. I tried sieving your two candidates using srsieve. In less than 2 minutes I was sieving higher than you got to. Forgive me for putting it this way, but two minutes of sieving on candidates that will take two days each to LLR test is pitiful. Switching to sr2sieve after ten minutes (it can use more than one core simultaneously on linux systems), I found the following:
51*2^21019467+1 is divisible by 200246537083. That's been verified (takes a fraction of a second) and so that candidate is proven to be composite. Sieving that took less than half an hour total.
I killed sieving on the other one at p=2281766902507 (2.28T) after a little over five hours of sieving. I needed that host for other things this morning. |
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These were checked for factors under 2^32 and came back negative. Can someone else run the LLR tests on these Proth numbers? I've tried and my LLR program glitches out around bit 131072.
29×2^21019467+1
51×2^21019467+1
If prime, these numbers could land in 11th and 12th in the list of largest known primes.
They're not PRP. They're not realistically going to be prime. You tested for factors under 2^32, i.e. 4,294,967,296 (4.2G). That's really small. We sieved SoB/PSP/ESP to 103,741,790,000,000,000 (103.7P) or about 25 million times as high. Primes are vanishingly rare for candidates that large. I tried sieving your two candidates using srsieve. In less than 2 minutes I was sieving higher than you got to. Forgive me for putting it this way, but two minutes of sieving on candidates that will take two days each to LLR test is pitiful. Switching to sr2sieve after ten minutes (it can use more than one core simultaneously on linux systems), I found the following:
51*2^21019467+1 is divisible by 200246537083. That's been verified (takes a fraction of a second) and so that candidate is proven to be composite. Sieving that took less than half an hour total.
If the other candidate sieves out I'll update this post.
Thanks for telling me. Guess NewPGen didn't go high enough to find that. Trying to find ways to test these things in the public domain is sorta hard.
I tested these candidates for hours on two different sieves and neither one went up to that value. At least applaud me for my attempt. I will keep sieving this n and if any come back with a "no-factor Trial Division" result I will post it to this thread and see if anyone will offer to sieve it further. |
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JimBHonorary cruncher
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I deliberately linked both programs I used so that you'd know where to get them. They're used here behind the scenes to start sieving and have been for years.
As far as giving you credit, yes, more power to you. But you're where I was five years ago: inexperienced. I'm sitting here behind the scenes at PG seeing just how rare primes of that size are. If it was as simple as us jumping to PPR24M to look for primes, we'd have done it years ago. I had the advantage of Lennart's experience for several years as to what programs were best for sieving. He knew them all. The ones I used are pretty inefficient when trying to sieve just two candidates, but I went with what I know works. We do a ton of sieving in order to reduce unnecessary LLR testing and I'm the guy who inherited the sieving. I linked both programs so that you could try them if you wanted to - they're available to everyone.
I wrote that first post at 2:50am my time, I'm not necessarily at my best then. No offense intended.
JimB |
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Can these programs be used on devices or just computers? When you have more time can you sieve these further?
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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JimBHonorary cruncher
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Can these programs be used on devices or just computers? When you have more time can you sieve these further?
They can be used on Windows or Linux computers. No, I have no intention of sieving those further. I don't generally sieve single candidates like that, I sieve tens of thousands or more at a time. I just happened to have an idle computer at the time I was reading your message. It's now doing other things. |
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Happen to know of anyone that can continue the sieving and then check for prime? |
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JimBHonorary cruncher
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Happen to know of anyone that can continue the sieving and then check for prime?
Yes: you. |
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compositeVolunteer tester
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And I thought comedy was dead in this forum! JimB, after I stop slapping my knees, I'll agree with you 100%.
NHM: mathematics is largely an individual pursuit. There are millions of unanswered questions and we're lucky when anyone can motivate a group to pitch in together in pursuit of a common goal. |
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29×2^21019467+1
51×2^21019467+1
The most urgent question: why do you focus on these two, and how did you come up with them? As JimB noted in his first post here, the second of them has a small factor which proves in an easy way it is non-prime. Is there anything interesting about the other one, n = 29×2^21019467+1? A priori, it is really, really unlikely that one specific number of this size is prime. 1/(log n) = 0.0000000686.
Take a look at the front page. PrimeGrid does have some sub-projects testing numbers of this size, picking candidates that are somehow considered more "interesting" than your numbers appear to be. By the nature of this, it takes many, many tries to find a prime in such sub-projects. Even with many participants with fast computers, it takes years to find just one prime in each sub-project like that.
If you give any reason why your n is particularly interesting, someone will soon test it. Otherwise, they will keep testing the numbers they prefer.
/JeppeSN |
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It was just of my interest to search at larger n. These numbers are semi-arbitrary, but I can tell you that 29×2^21019467+1 is the smallest number at this n that is even a candidate under 2^67. I'll try testing it again Tuesday using the sieves Jim gave me.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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It was just of my interest to search at larger n. These numbers are semi-arbitrary, but I can tell you that 29×2^21019467+1 is the smallest number at this n that is even a candidate under 2^67. I'll try testing it again Tuesday using the sieves Jim gave me.
You mean you look at k*2^21019467 + 1 for odd k and find very small factors for each k = 1, 3, 5, ..., 27? That is true.
One would expect A057778(21019467) to be much larger than 29, I think.
/JeppeSN |
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Yep, that's what I did to find these! Based on what BOI NC has already done with Proth primes, I wouldn't expect this or actually be a prime- more likely to be something in the thousands. Only thing is, the multiplier must be relatively prime to 21019467 (or whatever the power might be).
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Crun-chiVolunteer tester
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It was just of my interest to search at larger n. These numbers are semi-arbitrary, but I can tell you that 29×2^21019467+1 is the smallest number at this n that is even a candidate under 2^67. I'll try testing it again Tuesday using the sieves Jim gave me.
2^67=147573952589676412928
With what hardware you make such deep sieva file?
Even with fastest GPU, you will take great amount of time, and looking at your reported hardware, you have ancient one...
P.S on I7-2700K at 4GHz, you will need about 20 hours to do PRP test with Prime95 for candidate 29×2^21019467+1
____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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JimB ran the sieve on some spare CPU cycles yesterday night up to 2281766902507, I typed the wrong number into my powers of 2 calculator-it's only around 2^42. Most of the software I use is pretty old, but I do have a newer and faster CPU/GPU that doesn't run BOINC...
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Crun-chiVolunteer tester
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..... but I do have a newer and faster CPU/GPU that doesn't run BOINC...
So what you waiting for?
____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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Access to the computer. I only go to that house once a week.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Yep, that's what I did to find these! Based on what BOI NC has already done with Proth primes, I wouldn't expect this or actually be a prime- more likely to be something in the thousands. Only thing is, the multiplier must be relatively prime to 21019467 (or whatever the power might be).
If you are wondering about why the multiplier must be relatively prime, if it had a shared factor w there must be a factor, and it must be of the form wn+1. This the 51 number had to be composite because 51 shares the factor 3 with 21019467. (Note, I forgot this theorem while performing the sieves, giving me a false positive on that k.)
Proof:
If a number k*2^n+1 has a k and n sharing a common factor w (kw*2^wn+1), then we can apply modular arithmetic (mod w). Yielding the following result:
0(mod w)*2^wn+0(mod w)+1
If we then apply Fermat's little theorem we get that 2^wn is 1 mod w. By splitting the exponent up using power rules we get:
0(mod w)*1*2^0+1
Because 0*1*1 is zero, the factor yielded is wn+1.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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JimBHonorary cruncher
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If you are wondering about why the multiplier must be relatively prime, if it had a shared factor w there must be a factor, and it must be of the form wn+1. This the 51 number had to be composite because 51 shares the factor 3 with 21019467. (Note, I forgot this theorem while performing the sieves, giving me a false positive on that k.)
Proof:
If a number k*2^n+1 has a k and n sharing a common factor w (kw*2^wn+1), then we can apply modular arithmetic (mod w). Yielding the following result:
0(mod w)*2^wn+0(mod w)+1
If we then apply Fermat's little theorem we get that 2^wn is 1 mod w. By splitting the exponent up using power rules we get:
0(mod w)*1*2^0+1
Because 0*1*1 is zero, the factor yielded is wn+1.
Counterexample from our database:
3*2^10829346+1
I've got 1490 more primes where k and n share the factor 3 and 447 more where k and n share the factor 5.
2nd counterexample that I just found by playing around:
5*2^15+1 is prime! (6 decimal digits, Trial divisions) Time : 13.273 ms. |
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Well, at least if there is a factor this is correct. I tested that using the factor Jim gave me and it IS of the form wn+1 where w=3. (21019467=3*7*1000927)
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Here are the primes like that below 10^5:
193 = 3*2^6 + 1
577 = 9*2^6 + 1
2113 = 33*2^6 + 1
2689 = 21*2^7 + 1
4481 = 35*2^7 + 1
7681 = 15*2^9 + 1
9857 = 77*2^7 + 1
10753 = 21*2^9 + 1
12289 = 3*2^12 + 1
13441 = 105*2^7 + 1
15233 = 119*2^7 + 1
15361 = 15*2^10 + 1
23041 = 45*2^9 + 1
25601 = 25*2^10 + 1
26113 = 51*2^9 + 1
32257 = 63*2^9 + 1
61441 = 15*2^12 + 1
76801 = 75*2^10 + 1
81409 = 159*2^9 + 1
84481 = 165*2^9 + 1
86017 = 21*2^12 + 1
87041 = 85*2^10 + 1
87553 = 171*2^9 + 1
96769 = 189*2^9 + 1
/JeppeSN
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Well, at least if there is a factor this is correct. I tested that using the factor Jim gave me and it IS of the form wn+1 where w=3. (21019467=3*7*1000927)
Jim found that:
51*2^21019467 + 1 is divisible by 200246537083
This can be written as:
(3*17)*2^(3*7*839*1193) + 1 is divisible by (3*173*223*317*2729)*2 + 1
To me, the fact that 3 appears in all three odd products seems to be a coincidence.
/JeppeSN |
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No, it is not a coincidence. I'm sure there is some sort of math behind it, possibly relating to the relationship showed in that flawed "proof" (which, by the way, still works because the smallest factor of a prime is itself, and when itself can be written in the form showed, itself is indeed wn+1.)
____________
Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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And I checked for the next candidate, and it is 59. Sieving will take a while to complete on it because I'm currently focusing on the 29 one.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Update: Fully sieved out 29 and 59, no factors to 2^42. Next step: testing for primes. Both of them!
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Crun-chiVolunteer tester
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Update: Fully sieved out 29 and 59, no factors to 2^42. Next step: testing for primes. Both of them!
2^42 = 4398046511104
It is to low sieve depth for that kind of number. If you have recent GPU, you can make sieve with much more depth before even start of PRP testing.
Good luck...
____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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I won't have access to that CPU in quite a long time now, so I decided that it would be best not to wait another week on the sieve results. If I waited a week I would likely have a crashed CPU or something. I only have two hours to run so it was the best possible result. Next week I'll sieve out 59 a bit more.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Crun-chiVolunteer tester
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I won't have access to that CPU in quite a long time now, so I decided that it would be best not to wait another week on the sieve results. If I waited a week I would likely have a crashed CPU or something. I only have two hours to run so it was the best possible result. Next week I'll sieve out 59 a bit more.
PRP test will be done about day per candidate... so go for it :) ( if you have Intel CPU with AVX or even better AVX2)
____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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Reason I've gone off and started doing manual prime testing is because I felt like I was getting nowhere with BOI NC. With manual testing I could be more in control of the candidates chosen and thus more likely to find a prime, even if the odds are against me on certain n.
____________
Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Update: Fully sieved out 29 and 59, no factors to 2^42. Next step: testing for primes. Both of them!
Why are you sieving one k at a time? Newpgen can sieve a range of k's at the same speed as you sieve a single k.
Here are the 213 k's < 10000 that survived sieve up to 1.4T
1416353284168:P:0:2:1
29 21019467
59 21019467
107 21019467
141 21019467
149 21019467
275 21019467
297 21019467
305 21019467
309 21019467
347 21019467
401 21019467
549 21019467
551 21019467
555 21019467
569 21019467
639 21019467
647 21019467
677 21019467
815 21019467
845 21019467
899 21019467
935 21019467
999 21019467
1041 21019467
1079 21019467
1121 21019467
1137 21019467
1181 21019467
1275 21019467
1419 21019467
1439 21019467
1541 21019467
1619 21019467
1661 21019467
1727 21019467
1769 21019467
1779 21019467
1835 21019467
1857 21019467
1877 21019467
1911 21019467
1937 21019467
2051 21019467
2081 21019467
2177 21019467
2259 21019467
2289 21019467
2375 21019467
2405 21019467
2447 21019467
2469 21019467
2499 21019467
2507 21019467
2615 21019467
2639 21019467
2669 21019467
2691 21019467
2711 21019467
2735 21019467
2759 21019467
2787 21019467
2817 21019467
2879 21019467
2891 21019467
2975 21019467
2979 21019467
2987 21019467
2991 21019467
3015 21019467
3059 21019467
3069 21019467
3095 21019467
3117 21019467
3315 21019467
3339 21019467
3477 21019467
3509 21019467
3581 21019467
3585 21019467
3599 21019467
3629 21019467
3669 21019467
3735 21019467
3755 21019467
3777 21019467
3801 21019467
3815 21019467
3879 21019467
3885 21019467
3935 21019467
4011 21019467
4037 21019467
4049 21019467
4137 21019467
4211 21019467
4247 21019467
4251 21019467
4329 21019467
4385 21019467
4401 21019467
4407 21019467
4421 21019467
4427 21019467
4455 21019467
4497 21019467
4517 21019467
4589 21019467
4599 21019467
4629 21019467
4659 21019467
4707 21019467
4715 21019467
4749 21019467
4895 21019467
4967 21019467
5001 21019467
5049 21019467
5105 21019467
5127 21019467
5141 21019467
5189 21019467
5201 21019467
5229 21019467
5259 21019467
5267 21019467
5285 21019467
5307 21019467
5337 21019467
5457 21019467
5511 21019467
5537 21019467
5567 21019467
5607 21019467
5699 21019467
5709 21019467
5747 21019467
5777 21019467
5889 21019467
5927 21019467
5931 21019467
5985 21019467
5997 21019467
5999 21019467
6059 21019467
6137 21019467
6191 21019467
6219 21019467
6221 21019467
6269 21019467
6297 21019467
6381 21019467
6455 21019467
6459 21019467
6519 21019467
6545 21019467
6627 21019467
6689 21019467
6701 21019467
6869 21019467
6897 21019467
6951 21019467
7077 21019467
7107 21019467
7121 21019467
7161 21019467
7185 21019467
7217 21019467
7539 21019467
7565 21019467
7599 21019467
7617 21019467
7631 21019467
7679 21019467
7731 21019467
7865 21019467
7889 21019467
8051 21019467
8067 21019467
8135 21019467
8201 21019467
8265 21019467
8271 21019467
8321 21019467
8327 21019467
8369 21019467
8397 21019467
8415 21019467
8591 21019467
8639 21019467
8699 21019467
8745 21019467
8865 21019467
9021 21019467
9065 21019467
9081 21019467
9101 21019467
9105 21019467
9129 21019467
9189 21019467
9245 21019467
9297 21019467
9339 21019467
9387 21019467
9405 21019467
9597 21019467
9605 21019467
9677 21019467
9681 21019467
9821 21019467
9957 21019467
9965 21019467
9975 21019467
9999 21019467
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I don't know why I haven't been doing that. Now just if I could PRP test these quickly. Maybe we could find a way to split the workload?
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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No, it is not a coincidence. I'm sure there is some sort of math behind it, possibly relating to the relationship showed in that flawed "proof" (which, by the way, still works because the smallest factor of a prime is itself, and when itself can be written in the form showed, itself is indeed wn+1.)
Here are the factors of 437*2^437+1 (437=19*23)
5
89
439
221018152169
19482167094601
105-digit prime
Suffice to say, none of them are of the form 19x+1 or 23x+1. |
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Finished the LLR testing for 29. However, I cannot release the results until next Saturday. (Only way I know it is complete is because now BOI NC is running full blast on there.)
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Crun-chiVolunteer tester
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Finished the LLR testing for 29. However, I cannot release the results until next Saturday. (Only way I know it is complete is because now BOI NC is running full blast on there.)
You dont need to release at all, because your candidate is not prime.
How I know that ?
Since you say that you finish LLR , then you know is prime or not.
And if it is prime, I doubt you will wait 7 days to report huge prime on Top5000 prime list :)
Any of us when found prime, small or big , report immediately.
____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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I don't know because I have no access to the CPU. A prime is only considered discovered once a human sees it, and I haven't seen it.
Edit: I know LLR is done because BOI NC is reporting results, and they cannot compete with LLR even on a dual-core CPU.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Saw the OEIS sequence ended at n=1001 and decided to find the prime on that n. The k that yields it is k=363 and the prime is 77791524881723007500855658561756131446757989329821739900416278195687486311670362493
00620230201951930006337325381435845950858674774126199956524803319231165307656496204
52239169541570016327528144900339473624311174083808048936013150524795418490485194767
5978688642800429613721472057779805304843811315018366977
Now working on n=1002. No primes up to k=602.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Saw the OEIS sequence ended at n=1001 and decided to find the prime on that n. The k that yields it is k=363 and the prime is 77791524881723007500855658561756131446757989329821739900416278195687486311670362493
00620230201951930006337325381435845950858674774126199956524803319231165307656496204
52239169541570016327528144900339473624311174083808048936013150524795418490485194767
5978688642800429613721472057779805304843811315018366977
Now working on n=1002. No primes up to k=602.
No, already 153*2^1001 + 1 is prime.
If you take the PARI code of the OEIS entry and change to ispseudoprime, i.e.:
a(n) = k=1; while(!ispseudoprime(k*2^n+1), k+=2); k
then with:
for(n=1000,10000,print(n,": ",a(n)))
you really quickly get:
1000: 13
1001: 153
1002: 1479
1003: 429
1004: 567
1005: 1109
1006: 445
1007: 171
1008: 1863
1009: 393
1010: 1879
1011: 557
1012: 3931
1013: 165
1014: 273
1015: 1679
1016: 715
1017: 1005
1018: 75
1019: 755
1020: 93
1021: 993
1022: 1323
1023: 207
1024: 1125
1025: 413
1026: 763
1027: 629
1028: 277
1029: 1011
1030: 225
and so on.
/JeppeSN
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Whoa, I missed that one sieving too quickly. Still working on the 21019467 project though, it will be running alongside this.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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hello sir!
you asked earlier in the thread if we could work together.
That is what BOINC is for.
Massive sieving has already been done for us, not mainly by the PG "officials", but by other PG volunteers. So when we download a Proth task, we know we have a well sieved candidate to test.
The we run it, using world class software that the "official" PG folk have selected and pre-tested and fully understand (understand bwetter than I do, certainly). It is much more likely to be successful than tinkering around on our own.
But "Much more likely" in the way you are much more likely to win a lottery once than twice running... the chances for any of us are pretty small within the BOINC framework, and even pitifullyER smallER if we stubbornly stay on our own.
Finally, there is an advantage for the volunteers as a whole: we are not duplicating work (except to verify results) whereas you, working alone may well be working on a number that someone else has also found independently. Together, as a project-wide team, we can cover all the ground.
So my invitation to you is to re-join the BOINC mainstream, or join a group like GIMPS (who are even less likely than us to find a prime in any one run, but who have the advantage on us that they could find a new world's biggest prime. GIMPS is like a bigger lottery -- less chance to win but an even bigger prize).
Warm regards
River~~ |
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I am working in the mainstream at the exact same time.
Edit: With PPS-24M, I could just check t5k and see if #11 has changed to something on my n. Only problem is double checking.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Plus, working alone, you still need to share credit with the software codes you use unless you completely roll your own. The days of lone-wolf hunting for record primes are over unless you have a handle on some new mathematical theory. I imagine some academics are a little miffed at that - I know one (professional) mathematician who is annoyed by know-nothings getting top billing in T5K.
EDIT: I think the reason is, finding a record prime used to be a niche occupation and it required some head work, so it was worth a published paper. Now it doesn't count, using established methods. |
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I am working in the mainstream at the exact same time.
Edit: With PPS-24M, I could just check t5k and see if #11 has changed to something on my n. Only problem is double checking.
Guys, lets be realistic.
Even if this member are mathematical genius, and he make new theory ( and I am thinking, he is not, and have few arguments) he just wont to have our attention. And he is succeeded in that part ( but only that part)
So to be clarified.
Lets say he have new theory. If he had new theory then it is easy for him to give us lets say 50 PRP of 500000 digits. Those PRP can be tested and verified on any modern computers in 20 hours.
Why 50 PRP of 500000 digits? Because, he can always find one , or two or three , and not publish it to the TOP 5000K. But 50, that will not be case.
Then , he can give us lets say 25 PRP of 1M. All that will immediately got attention of all math world , and every one will listen what he need to say.
But no, he came with different approach. He just write claim that he found two PRP . One was immediately eliminated, and even that casts doubt on his words.
Second PRP can be verified in one day on quad core to be PRP or not. But as usual, he has very old computers ( but even on them) he can prove PRP in lets say 10 day. But no: he put those computers to the BOINC, and his "hidden" daddy "beast" is unreachable until next weekend, and we all, must wait until he see results of PRP.
When one member of this forum read his statement he answer to me: It's sad, not funny.
And I think that talks everything.
I am just sorry that his forum dont have ban option....
____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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Why does the whole world hate me? Seriously... Do not ban me. I might have failed to you in trying to prove something with known counterexamples, and don't have hands on any new theory. I'm only 14, and I know less than you. But do I not have the right to go out on my own to try finding primes too? Yes. This was my first attempt. I am learning boinc. And as to your claims about Daddy, it is just a side effect of family separation. If you saw me in person right now, you would see a very sad person- because all of my friends here at boinc are abandoning me. What would you say if I said I had sieved out 20 primes larger than the Gimps record by hand? I have- it's something called modular testing and I did double check it by CPU in mostly under a minute's time.
____________
Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Crun-chiVolunteer tester
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[quote...What would you say if I said I had sieved out 20 primes larger than the Gimps record by hand? I have- it's something called modular testing and I did double check it by CPU in mostly under a minute's time.[/quote]
What I would say? That you are 14 old year that wont some attention.
Or you are new Albert Einstein ?
In first case you will be ( if I am moderator of this forum) banned forever in second case I will say Prove it.
Can you prove it?
You cant
So .... you know what you must do.
Dont waste ours and your time, and for first find few 1 M prime for beginning. If you can double check world highest prime in minutes then you can also check your "prime " in seconds. But you didnot! Why? Because you didnot find anything, and didnot have any theory.
This is my last post here... because you are...... ( on those ..... you can add any negative words ) and I wont to be banned for writing them.
Best regards, and I wish you happy dreams about bigger prime then GIMPS has it.
____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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I can prove it.
All even powers of 2 minus one are divisible by 3.
2^2n -1
2^(2n+0)-1
Because we are testing for divisibility by 3, we can eliminate 2^2n.
2^0-1=0 mod 3.
All powers of 2 minus one that are multiples of 3 are divisible by 7.
2^6n-1
2^(6n+0)-1
2^0-1=0 mod 7.
For all other multiples of 3, use this:
2^6n+3
2^(6n+3)-1
2^3-1=7= 0 mod 7
Only numbers of form 2^4n-1 are divisible by 5.
2^4n-1
2^(4n+0)-1
2^0-1=0 mod 5.
And this can be continued, as 11 will follow the form 2^10n-1, 13 follows the form 2^12n-1, etc.
An example of each:
2^6-1=63=3^2(7). Both a multiple of 3 and of 7, follows both rules.
2^10-1=11*31*3. Follows rule for 3 and 11.
2^12-1=4095=5*3^2*7*13. Follows rule for 5, 3, 7, and 13.
Now there's a sneaky thing to do with the prime powers, and that is pretty famous. All prime powers of 2 minus one are either prime or have a factor of the form 2kn+-1.
Why are all of the multiples of 6 also divisible by 3^2? 6 is equal to the Euler totient function of 9 minus one, so thus you can use Euler's Theorem to yield the following result:
(2^(kphi)-1
2^6k-1 (phi(9)-1=6)
2^0-1=0 mod 9.
____________
Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Michael GoetzVolunteer moderator
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Why does the whole world hate me? Seriously... Do not ban me. I might have failed to you in trying to prove something with known counterexamples, and don't have hands on any new theory. I'm only 14, and I know less than you. But do I not have the right to go out on my own to try finding primes too? Yes. This was my first attempt. I am learning boinc. And as to your claims about Daddy, it is just a side effect of family separation. If you saw me in person right now, you would see a very sad person- because all of my friends here at boinc are abandoning me. What would you say if I said I had sieved out 20 primes larger than the Gimps record by hand? I have- it's something called modular testing and I did double check it by CPU in mostly under a minute's time.
The world doesn't hate you. :)
And welcome to the world of mathematics and computing.
I admire your enthusiasm and your nobody should be blaming you for not knowing things at 14 that many of us didn't know at 40! None of us were born knowing what a prime number is. We all had to learn it.
One thing that you might want to consider as part of the learning process is that there's always a reason that people do things the way they do -- and conversely why people don't do some things. Rather than starting with "This is what I want to do...", perhaps a better way of introducing yourself would be "Is this a good way of approaching this problem?"
Such a question would likely have been answered with plenty of advice about the known best practices for sieving and searching for primes. Instead, you presented an approach that appeared to many to be naive and unwise, and you received critical comments about your approach. That's both expected and desirable -- constructive criticism helps everyone. Of course, some people are more polite than others. It's a big world, and everyone's different. (And, also, English isn't everyone's first language, so sometimes people may seem more rude than they actually are because of the language nuances.)
I personally think it's GREAT to see someone like yourself here. We need more 14 year olds hunting for prime numbers. You're our future, after all.
On a side note -- electronic communication tends to be a lot harsher than other types of interaction. I've been online for over 20 years, and it's VERY easy to offend someone inadvertently, or to take offense at some perceived slight that wasn't actually intended. You need to both have a thick skin and not take things very personally, and also be very careful about what you say and how it may be received by the reader as opposed to how it was meant by the writer. (And I say this not a day after I totally lost my cool and kind of exploded privately at someone here. You know who you are, and I apologize. Maybe I should take my own advice?)
Anyway, welcome to the community!
(By the way, I think your communication skills are excellent -- your teachers and parents should be proud of you. And I think the rest of us really need to chill a little bit.)
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My lucky number is 75898524288+1 |
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He's probably more mad about the fact that my family broke up a little after I was born and my computers are on the side I don't live with.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Crun-chiVolunteer tester
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He's probably more mad about the fact that my family broke up a little after I was born and my computers are on the side I don't live with.
Nobody here doesnot talk about your private life. It is obvious that you have, and you will have hard life.
I am talking about you constantly say that you have prove, and you are not giving results, just writing "proof".
Does you really mean that someone smarter, better educated , and older doesnot have and got same idea as you?
But still we make factoring, but still we search for big primes years and years, with computer resources that you cannot imagine.
So , since your thread is started with claim that 29×2^21019467+1 and 51×2^21019467+1 is PRP , and since we eliminated one PRP after just more sieving then you willing to do BEFORE you say you find PRP, and since you claim that you if I said I had sieved out 20 primes larger than the Gimps record by hand? I have- it's something called modular testing and I did double check it by CPU in mostly under a minute's time. then I ask you that give me 10 PRP numbers in base 2, size one milion digits. I will verified them in 10 hours on my 12 cores I then I will shut up and will never say word again and will apologize to you on this forum.
But if you cannot do that... dont claim that
Best regards
____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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Slowly making progress on this task. Sieved out 8 candidates by hand (that's all I've had time for so far- been away from either home)
Edit: Numbers are not mega-candidates. They are 993,434 digits long- close enough to a million right)
Oh My stumbled across this candidate and it cannot be tested using modular test.
11•2^3299618-1 no factor to 2^32. Will need CPU power to get to optimal depth.
____________
Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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77 11*2^4643238-1 1397755 L2484 2014
L2484 Ritschel, PSieve, Srsieve, Rieselprime, LLR
source: http://primes.utm.edu/primes/lists/all.txt
Also: http://www.mersenneforum.org/showpost.php?p=440357&postcount=893
You can guess that Thomas or someone else has done sub-mega tests.
Unfortunately, prothsearch.com/riesel2.html seems to be down. |
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Why does the whole world hate me? Seriously... Do not ban me. I might have failed to you in trying to prove something with known counterexamples, and don't have hands on any new theory. I'm only 14, and I know less than you. But do I not have the right to go out on my own to try finding primes too? Yes. This was my first attempt. I am learning boinc. And as to your claims about Daddy, it is just a side effect of family separation. If you saw me in person right now, you would see a very sad person- because all of my friends here at boinc are abandoning me. What would you say if I said I had sieved out 20 primes larger than the Gimps record by hand? I have- it's something called modular testing and I did double check it by CPU in mostly under a minute's time.
The world doesn't hate you. :)
And welcome to the world of mathematics and computing.
I don't hate you at all.
My posts in this thread are in no way meant to be hateful. I just try to be informative and friendly and correct some things you wrote that were incorrect or easily misunderstood. I hope and think you will learn a lot from this forum. I think it is safe to say everyone here has learned from this forum.
/JeppeSN |
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That's the wrong power. 3299618, not 4643238.
Found another one, sieved to the same depth on same n:
15*2^3299618+1. Only 8 more CrunChi!
____________
Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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That's the wrong power. 3299618, not 4643238.
I think Paul Underwood meant to say that when these guys found the larger prime, they probably also tested your smaller candidate earlier in the process. If that is correct, there is no need to test it again. /JeppeSN |
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Crun-chiVolunteer tester
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That's the wrong power. 3299618, not 4643238.
Found another one, sieved to the same depth on same n:
15*2^3299618+1. Only 8 more CrunChi!
sr0 --newpgen --v --nmin 3299610 --nmax 3299718 --pmax 25000000 "15*2^n+1"
25000000:P:1:2:257
15 3299617
15 3299625
15 3299627
15 3299652
15 3299658
.....
So "yours" candidate dont even survive 25000000 deep sieve: so once again...
you are wrong
Lets see next candidate
You say 11*2^3299618-1
Once again your candidate doesnot survive
25000000:M:1:2:258
11 3299670
11 3299678
11 3299682
11 3299702
And to be totally sure
15*2^3299618+1 is not prime. RES64: D6692629E572AEF5.
so... do you want to continue embarrass yourself, be my guest
____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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so... do you want to continue embarrass yourself, be my guest
I know it's tempting to shoot down what appear to be obvious errors but there's probably a way to offer corrections and suggestions without making someone feel small and insignificant.
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Crun-chiVolunteer tester
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so... do you want to continue embarrass yourself, be my guest
I know it's tempting to shoot down what appear to be obvious errors but there's probably a way to offer corrections and suggestions without making someone feel small and insignificant.
I fully agree with you,and you suggestion is OK if someone read suggestions, and wants to learn.
I do not understand math much more then this kid,but also, I do not develop breakthrough ideas like he does. I know what I know, I learn slowly and results is here. Since only I respond to his reply, it looks like I humiliate him, but that is not true. I just wont to point them to right direction, and he in other side wont stop to force his believe ( and these beliefs is wrong, as we all see).
____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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This is just embarrassing!!!!
When posting to this thread; please just take a step back, think prior to responding and dump the bitchy, sanctimoniousness, sententiousness and "holier-than-thou" attitudes that are dominating this discussion.
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There's someone in our head but it's not us. |
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Nathan,
Your high school must have computing facilities which are sitting idle during the evening and especially during weekends. With Christmas and New Year approaching, one would expect even greater availability since exams and holidays are just around the corner.
Are you not able to get access during these windows of opportunity using, for example, the software suggested in this thread?
It is really good seeing someone your age actively involved with mathematics! |
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Obviously, this guy is the only one that is not on my side. It is sorta embarrassing to see the things that work fail, and these ideas are not breakthroughs. The modular test was something thought up and proven by someone else 2 years ago. I could ask and have asked my maths teachers if these are valid conclusions and thus true statements- except the one that obviously has counterexamples- and they're all true. Gonna hold my ground and continue manual prime testing as a hobby. And CrunChi, you interjected before I even sieved these to any depth that would have been useful. Today was a busy day. I'm not trying to become Pierre de Fermat.
____________
Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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There is a long and discouraging history of smart people trying to invent predictors of prime numbers of various forms, and all we have in the end are efficient tests of primality. This interesting read describes a relatively recent breakthrough. AKS Primality Test (PRIMES is in P) From the commentary in the references, it seems the method was established in 2002, and the AKS paper was finally published in 2004. |
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Dave
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This is just embarrassing!!!!
When posting to this thread; please just take a step back, think prior to responding and dump the bitchy, sanctimoniousness, sententiousness and "holier-than-thou" attitudes that are dominating this discussion.
Hear hear. A lot of us invest a lot of time, money & planning into these subprojects. PG is not the place for arguments. If you want to argue go on Chat-Scene.
Nathan: keep up your innovations - you may end up on an unexpected tangent & discover something. |
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If anyone is interested, 15*2^3299618 + 1 has two very small prime factors, 1193 and 3393053. And the other one, 11*2^3299618 - 1, has three very small ones, 19139, 26801, and 648873851. /JeppeSN |
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These were just desperation attempt
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Even my maths teachers say a proof is more powerful than an example. If you just say "2^21-1 is divisible by 7," then you haven't really done anything but show it for one n, and that one could be a false positive. If you can prove, however, that 2^3n-1 Is always divisible by 7, then you've generalized your case and now you can say without any doubt that the statement holds for all n (or whatever you're trying to prove holds true on its full interval).
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Even my maths teachers say a proof is more powerful than an example. If you just say "2^21-1 is divisible by 7," then you haven't really done anything but show it for one n, and that one could be a false positive. If you can prove, however, that 2^3n-1 Is always divisible by 7, then you've generalized your case and now you can say without any doubt that the statement holds for all n (or whatever you're trying to prove holds true on its full interval).
Yes.
If you have a claim that something is true in general, you would want to either prove the claim, or disprove it.
To prove it, you need to come up with a general argument that holds logically in all cases (with the full generality of the claim). That is a proof. In contrast, coming up with a single example that "corroborates" the claim is far from enough.
To disprove the claim, it suffices to come up with a single counterexample. That demonstrates that the claim was not correct in general.
It will not be possible to both prove and disprove the same claim (or if that ever happened, we would know that mathematics was "broken", that the axioms that are underneath it all were mutually inconsistent).
In mathematics it sometimes happens that people construct something that appears to be a (valid) proof. But then later, someone finds a counterexample to the "theorem" that had been proved. In such cases it is necessary to examine the "proof" more carefully to find out why it is wrong.
Note: A counterexample is usually simple to check (but could be extremely hard to locate). A proof is usually more difficult to grasp and verify, and errors happen sometimes.
/JeppeSN |
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This seems to be the one thing he disagreed on(CrunChi). By the way the example I used its factorization:
2097151=7^2*127*337. In case anyone wanted to know:)
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Even my maths teachers say a proof is more powerful than an example. If you just say "2^21-1 is divisible by 7," then you haven't really done anything but show it for one n, and that one could be a false positive. If you can prove, however, that 2^3n-1 Is always divisible by 7, then you've generalized your case and now you can say without any doubt that the statement holds for all n (or whatever you're trying to prove holds true on its full interval).
2^3n-1 is always divisible by 7, because 8 ≡ 1 (mod 7).
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DeleteNull |
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I know. Just used that as an example. Plus I posted another attempted one for this exact theorem down on Sunday.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Crun-chiVolunteer tester
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I know. Just used that as an example. Plus I posted another attempted one for this exact theorem down on Sunday.
Lets see your history here :)
1. you say that you find those two PRP: one is eliminated immediately .....
2. then you say I had sieved out 20 primes larger than the Gimps record by hand? I have- it's something called modular testing and I did double check it by CPU in mostly under a minute's time.
3. then I ask you ten mega primes on base2: you give me nothing-again you claim to search to 2^32 or 2^42
4. And last, after all : you say for your attempts : These were just desperation attempt
And now lets analyze those statements:
1. first statement -what to say: it looks like you dont know what sieve is at all, because: if you sieved at all: you fill claim: I am found one prp no two.
2.second statement: you, 14 old guy sieved 20 primes larger then GIMPS record by hand, and can check them under minute? - now is 2016: fastest supercomputer maybe can check it under minute, but yours cannot, and definitely you cannot sieved it by hand
3.statement - I am still waiting my requested mega primes.... if you can sieved largest primes by hand, then you can give me ten megaprimes in seconds...
4 statement: what to say: you say enough.
Please dont say I am hating you, or something else like that: I dont hate anything or anyone, and certainly not some 14 old guy. Hate is very bad filing.
But I was not open new thread ,and say : hey guys I have found few PRP, I was sieving up to 400P ( above 2^58) , and they have no factors: will you checked for me?
Because those files, are public , and Primegrid sieved long time ago: better and deeper that we can sieve as persons in many years.
I myself: search for repdigit primes: and in average for 500000 digit prime you must process 20.000 candidates.
So before post something here, and telling that you have proof , look around, learn, search...there is no better and faster way.
P.S On the other forum, one "smart" guy wrote this statement: very fast way to find primes is to : sieve sequence, and then from sequence remove any N that is not prime. After that you got very small numbers of candidates that has need to be checked. And that what I calling is quasi-math!
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92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
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P.S On the other forum, one "smart" guy wrote this statement: very fast way to find primes is to : sieve sequence, and then from sequence remove any N that is not prime. After that you got very small numbers of candidates that has need to be checked. And that what I calling is quasi-math!
Yes, be careful with claims if you want people to consider what you have to say.
A person once claimed on a PG forum (and was ignored) that an extremely fast way to multiply numbers is to use lookup tables, and that the security agencies do it this way. The first claim is surely correct, and the second is lacking evidence. However he neglected to mention how much storage is needed for this classic time-space tradeoff.
In doing LLR, the table of products must be stored in original form, not as modular residues, because each residue is going to be used exactly once so there is no point to saving them as residues. I can't imagine how vast this table would be for the large numbers we are dealing with, considering that every squaring roughly doubles the number of bits needing to be stored, and the squaring is done millions of times to test a single record prime candidate.
It's the reason that lowly 64-bit multiplications are done with hardware rather than lookup tables. A 64-bit lookup table would need 2^64 x 2^64 x 2^7 bits = 2^127 bytes. Let's try to visualize that. A one terabyte hard disk has about 2^40 bytes on it, so you would need 2^87 one-terabyte hard disks in the storage array.
The age of the earth is around 2^67 milliseconds - not even close to the number of one-terabyte hard disks needed to store a 64-bit multiplication table. |
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2^3n-1 is always divisible by 7, because 8 ≡ 1 (mod 7).
I like this very concise presentation. Just to repeat:
2^(3n) - 1 is the same as (2^3)^n - 1 = 8^n - 1, and taken modulo 7, that is 1^n - 1 = 0.
We should generalize this to:
2^(m n) - 1 is the same as (2^m)^n - 1, and taken modulo 2^m - 1 that is 1^n - 1 = 0.
If we write MERSENNE(x) = 2^x - 1, this shows that MERSENNE(m n) is divisible by MERSENNE(m).
So MERSENNE(x) can be prime only if x is prime. (x cannot be written x = m n for m>1 and n>1.)
/JeppeSN |
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The record numbers were not primes. They were numbers easily sieve-tested by the methods described in the post. As for 10 PRP base 2, I'll send those when I get access to my dad's CPUs again. But I have taken out some candidates on both sides -1 and +1.
The n I searched Sunday was 3299618, and the eliminated candidates were:
3+
3-
5+
5-
7+
7-
9+
9-
11+
13+
13-
15-
17+
Thanks to some people on here the following were eliminated:
11-
15+
17-????
I do know what a sieve is. I just didn't know the depth needed to go through with it until after the post thanks to jimb. I don't hate you CrunChi- just please don't harass me like that. Someone new wanting to do a manual test has to learn some things and that was what this post was for. Learning the dos and donts of sieving and testing.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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So quick test on N you say that was you research gives those results
25880733418:P:0:2:1 -on + side
129 3299618
217 3299618
255 3299618
267 3299618
297 3299618
357 3299618
373 3299618
435 3299618
475 3299618
487 3299618
555 3299618
559 3299618
615 3299618
657 3299618
699 3299618
787 3299618
819 3299618
847 3299618
853 3299618
855 3299618
879 3299618
925 3299618
927 3299618
949 3299618
969 3299618
25859450598:M:0:2:2 on minus side
105 3299618
215 3299618
243 3299618
281 3299618
533 3299618
545 3299618
551 3299618
563 3299618
573 3299618
617 3299618
633 3299618
645 3299618
711 3299618
713 3299618
755 3299618
797 3299618
813 3299618
815 3299618
837 3299618
857 3299618
945 3299618
951 3299618
995 3299618
Those are K between 2 -1000 that was left after sieved
When you use much more sieved data from Primegrid you got those results
100000000000000000:M:0:2:2 minus side
281 3299618
563 3299618
573 3299618
633 3299618
713 3299618
837 3299618
857 3299618
945 3299618
995 3299618
same range as before: from 2-1000.
those test can be done in two minutes for plus side, and same time for minus side....
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92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
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Weirdly my LLR test stopped running and I had to restart it today, halfway done with the test of 29.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Weirdly my LLR test stopped running and I had to restart it today, halfway done with the test of 29.
You dont need to test it : it is not prime....
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92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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So you've tested it Crunch? Or are you still saying these things because you don't like my approach to the problem?
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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So you've tested it Crunch? Or are you still saying these things because you don't like my approach to the problem?
Your approach is wrong, and I still mean that your approach to problem is way off the road. And since you cannot give me smaller candidates that is prime, testing such huge candidates is pure waste of time.
My suggestion: start with smaller ones: start with "PRP" that has 100000 numbers. When your "method calculate" 100 such primes, then we can go to next lever and calculate 100 PRP of 500000 numbers and so on.
In mean time.... learn
And for your question does I or doesnot I tested that PRP, I will not yes or no.
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92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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I've disregarded the project on 21019467. It was too large for my clunky computers to handle within a week. I've gone on and started doing more manageable projects, doing work on that other n I was working on Sunday. I've found candidate on it: 1065(2^3299618) plus or minus 1. Sieved very well. In fact I can give you finite list of about 200000 on that K in a few minutes. That is, TWIN prime candidates.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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I've disregarded the project on 21019467. It was too large for my clunky computers to handle within a week. I've gone on and started doing more manageable projects, doing work on that other n I was working on Sunday. I've found PRP on it: 1065(2^3299618) plus or minus 1. Sieved very well. In fact I can give you finite list of about 200000 on that K in a few minutes. That is, TWIN prime candidates.
Ok give me only 10 candidates... but be careful this time: dont say as last time: it was desperation attempt
10 candidates can be tested in 5 hours
Waiting....
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92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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I'm going out to 1.4T with the sieving effort. So far over 20 million candidates are gone and only 200000 are left. Only 20K left to that point and then I'll turn the LLRing on.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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I'm going out to 1.4T with the sieving effort. So far over 20 million candidates are gone and only 200000 are left. Only 20K left to that point and then I'll turn the LLRing on.
You are again twisting your words: what indicating that you are young person. If you proof something, them give that proof: again you just sieving and claim that 1065(2^3299618) plus or minus 1 is PRP: and it is PRP ( because it will survive sieving ( at least minus side) to much more deep sieve depth then is your 1.4 T
Primegrid release data that is sieved to 100P and to 400P. You dont need to sieve , since it is presieved, and it is available to public.
So start using that data, and you will save alot of time.
Than , with your "algorithm" you can search much faster.
____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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Again, sieving essentially does that exact same method in a quicker way so even though I am sieving doesn't mean sieving isn't based on modular testing. Anyway here are your PRP:
1065 3299618
1455 3299618
1497 3299618
1575 3299618
3147 3299618
5565 3299618
9345 3299618
9705 3299618
10185 3299618
13203 3299618
16803 3299618
18603 3299618
18963 3299618
20157 3299618
21717 3299618
23997 3299618
24627 3299618
26037 3299618
29427 3299618
33837 3299618
34017 3299618
35703 3299618
39165 3299618
40755 3299618
43593 3299618
44955 3299618
47313 3299618
47625 3299618
48885 3299618
52503 3299618
54627 3299618
55677 3299618
59553 3299618
62973 3299618
64053 3299618
66123 3299618
66273 3299618
70083 3299618
70455 3299618
70923 3299618
71907 3299618
75495 3299618
80787 3299618
86433 3299618
87093 3299618
88395 3299618
89505 3299618
90135 3299618
91875 3299618
92985 3299618
93765 3299618
98865 3299618
98955 3299618
104175 3299618
106035 3299618
107493 3299618
108315 3299618
109227 3299618
110355 3299618
113145 3299618
114183 3299618
114597 3299618
115623 3299618
115707 3299618
117657 3299618
117975 3299618
118005 3299618
120837 3299618
121695 3299618
122763 3299618
122913 3299618
123417 3299618
124047 3299618
124125 3299618
124503 3299618
124653 3299618
127413 3299618
128415 3299618
131613 3299618
137703 3299618
138957 3299618
144705 3299618
145137 3299618
146787 3299618
148473 3299618
149883 3299618
154263 3299618
Big gap, lots of candidates in here.
450999147 3299618
All are twin candidates: check on both sides.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Once again , without any testing I can say that 5565 3299618 and 9705 3299618 are not primes at least on minus side, and also, cannot be twin primes as you said it will be.
So your method is bad method, and your way is wrong way.
____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
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Since you are so sure, what are the factors? If they are like 3, 5, 7, etc I don't know why the sieve didn't eliminate them.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Since you are so sure, what are the factors? If they are like 3, 5, 7, etc I don't know why the sieve didn't eliminate them.
Primegrid eliminated and verified it: so it is true: factor is below 100P
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92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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So are you going to verify these PRP as prime or not? Even though two were composite I still accomplished your goal by findin 10 PRP.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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So are you going to verify these PRP as prime or not? Even though two were composite I still accomplished your goal by findin 10 PRP.
I will not.
Why ?
You didnot find anything, and you have not any "secret" algorithm. You have "your method" and that method obviously is not better then sieving.
And I have millions of candidates left by Primegrid , sieved better and deeper you will ever get.
So sieving is produced list of candidates ,but they are not PRP.
PRP is number that is probably prime, not 100% but it is 99.99%
You will not give me 10 PRP-s , you give me 10 candidates, and in your candidates there is no difference, will I use them or will I use data from Primegrid.
I must, and I will repeat your claim at the beginning of this thread, that you found PRP, not candidates, and that is big difference.
And since we eliminated one immediately, and now I eliminated two immediately, I have reasonable doubt that you have "some secret method" that works better then sieving.
If your method produce PRP, then it will be produced 99.99% primes.
And as we can all see it just list of candidates not PRP.
Last thing before I lose the desire to respond to you is next thing: and will repeat it again: lower your N ( so candidate is 50000 or 60000 digits long - N is on base 2 in in range 170000 - 200000 ) give me 50 "yours PRP" and I will verified 50 candidates in few minutes. I will you list of results: and you can just hit one or two prime by pure luck. But you will not hit 50 PRP.
So I am waiting: give me 50 PRP: I will verified him and expect since you "have your special method" that at least 45 of them are primes. And in mathematics is still not proof: for that you must give me 50/50.
Can you accomplish that or not: you claim you do it.
____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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Before I become so tired of you that I'm on the verge of blocking every post from you, let's agree to something. Let me crunch what I wish to crunch, and you can crunch what you want to crunch. There is no reason that the numbers I crunch should be controlled by an angry guy like you. My computers are all sitting and testing prime candidates- one testing base 3 numbers about your size you asked for and the other doing those sub mega twins.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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I wish you luck.
Best regards
____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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Just put my new 6-core on the job with the smaller 20000 digit candidates for a couple hours. It took it half a minute to perform the primality tests using LLR. Unfortunately no PRPs to report back. Still waiting till Saturday to see those sub mega twins though.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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I found 2 PRP:
2^9004-59
2^9584-59
These have been tested using LLR and I need a Linux computer to run Primo tests on these 2.
2^9004-59 is base 3-Strong Fermat PRP! (2711 decimal digits) Time : 35.745 sec.
2^9004-59 is strong-Fermat, Lucas and Frobenius PRP! (P = 5, Q = 5, D = 5) Time : 71.941 sec.
Candidate saved in file t3014534.in for further test with Primo.
2^9584-59 is base 3-Strong Fermat PRP! (2886 decimal digits) Time : 37.592 sec.
2^9584-59 is strong-Fermat, Lucas and Frobenius PRP! (P = 5, Q = 3, D = 13) Time : 84.455 sec.
Candidate saved in file t5135522.in for further test with Primo.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Crun-chiVolunteer tester
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I found 2 PRP:
2^9004-59
2^9584-59
These have been tested using LLR and I need a Linux computer to run Primo tests on these 2.
2^9004-59 is base 3-Strong Fermat PRP! (2711 decimal digits) Time : 35.745 sec.
2^9004-59 is strong-Fermat, Lucas and Frobenius PRP! (P = 5, Q = 5, D = 5) Time : 71.941 sec.
Candidate saved in file t3014534.in for further test with Primo.
2^9584-59 is base 3-Strong Fermat PRP! (2886 decimal digits) Time : 37.592 sec.
2^9584-59 is strong-Fermat, Lucas and Frobenius PRP! (P = 5, Q = 3, D = 13) Time : 84.455 sec.
Candidate saved in file t5135522.in for further test with Primo.
On Internet you can find old version of Primo for Windows, but even then you will need to at least hour or two per each candidate to test and verify it is prime. I dont know why you even bother with such small PRP?
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92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
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I just checked WolframAlpha and these are previously proven primes. I've decided it's better to go for primes than for T5K.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Crun-chiVolunteer tester
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I just checked WolframAlpha and these are previously proven primes. I've decided it's better to go for primes than for T5K.
Then go for primes in form k*b^n+1 or k*b^n-1 ( so you can prove it yourself)
In that case LLR will prove it or not, much more faster then Primo
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92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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I just checked WolframAlpha and these are previously proven primes. I've decided it's better to go for primes than for T5K.
How did you ask Wolfram Alpha to get that answer?
I do not think Wolfram Alpha keeps lists of "ordinary" primes of this kind and size. If I ask isprime(2^9004-59) or isprime(2^9584-59), I get no answer.
Given the probable-primality you found, it is extremely likely these two numbers are prime.
/JeppeSN |
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I typed Is it prime? And after about a minute the result came back after exceeding standard time.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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I just checked WolframAlpha and these are previously proven primes. I've decided it's better to go for primes than for T5K.
How did you ask Wolfram Alpha to get that answer?
I do not think Wolfram Alpha keeps lists of "ordinary" primes of this kind and size. If I ask isprime(2^9004-59) or isprime(2^9584-59), I get no answer.
Given the probable-primality you found, it is extremely likely these two numbers are prime.
/JeppeSN
I get an answer from Wolfram. It takes a few seconds. It is doing a PRP test not really a primality test. So there is some remote chance it will be wrong! |
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OK guys, it appears I did not wait long enough for the answer.
As far as I could understand, a function PrimeQ of Mathematica is used, which uses "the multiple Rabin-Miller test in bases 2 and 3 combined with a Lucas pseudoprime test."
That sounds just like the ispseudoprime function of PARI/GP which I am more familiar with. With that software, ispseudoprime(2^9004-59) says yes (1) in about 0.7 seconds, and ispseudoprime(2^9584-59) in about 0.8 seconds.
In PARI/GP you can do a deterministic primality test with the isprime function (slow); apparently such functionality does not exist in Mathematica?!
/JeppeSN
ADDITION:
And if you run the PARI/GP code:
for(n=6,10^10,ispseudoprime(2^n-59)&&print("2^",n,"-59"))
for some time, you get:
2^6-59
2^8-59
2^20-59
2^48-59
2^64-59
2^108-59
2^124-59
2^184-59
2^9004-59
2^9584-59
2^17768-59
so there is your next number :-) Just as an example of what GP will do. |
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Went back to by-hand work and then found a thread on the Mersenne Forums about modular residues, which really sped up the process, was able to trial factor another number, but with the limited range of even that sieve, wasn't even close to 2^32. That depth is unreachable by hand, would require squaring huge numbers. FYI I will NOT test this new number, it is too big for my computer to hsndle.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Crun-chiVolunteer tester
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Went back to by-hand work and then found a thread on the Mersenne Forums about modular residues, which really sped up the process, was able to trial factor another number, but with the limited range of even that sieve, wasn't even close to 2^32. That depth is unreachable by hand, would require squaring huge numbers. FYI I will NOT test this new number, it is too big for my computer to hsndle.
I hope that number finished with -1 or +1: so it can be fully tested
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92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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Is this a coincidence or a discovery?
The last digit of the powers of 2 cycle every 4th number. The last two cycle every 20th number. The last three cycle every 100th. This means that the last n digits cycle every 4×5^(n-1)th number or does it?
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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It did.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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FACTORED! Divisible by 12473.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Factors of numbers I've tested today:
2^2197022+159 factor: 12473
161×2^2197022-1 factor: 26111
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Proth/Riesel Search n=2197022 Status.
All numbers up to 10002 have been tested. No primes were found.
Leading edge candidate is 10003*2^2197022+1. Potential Prime Rank:~700.
Trailing edge candidate is 99997*2^2197022+1.
LLR tests have been done by PrimeGrid up to 9999. No LLR test was needed for either 10001 candidate, both had very small divisors. Needed siever for 10003*2^2197022+1. Once more candidates are tested and trailing edge is found this post will be updated.
Oh and to add, my favorite number divides one of the 10001 candidates, so that's cool I guess.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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This was already discovered, the proof is here:
http://www.exploringbinary.com/cycle-length-of-powers-of-two-mod-powers-of-ten/
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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compositeVolunteer tester
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This was already discovered, the proof is here:
http://www.exploringbinary.com/cycle-length-of-powers-of-two-mod-powers-of-ten/
This is very good of you. When you are discovering stuff on your own, even if it was previously discovered, it means you are thinking. Many people never get past rote memorization.
It's a hazard of science. The trick to producing a good math paper is finding out what other people have already done that is similar, but not exactly the same. The references show the boundaries of what you are claiming as new discoveries, often extending the prior work of others or of yourself.
It's all great to be working in isolation, until you find out that your discovery was already published, sometimes in such an obscure reference that experts in the field didn't notice, or it was too advanced so that nobody but the author understood it at the time of publication. Or many years after the initial discovery and its disappearance, someone rediscovers it and receives credit, but eventually the obscure reference is unearthed and the recognition ends up being shared.
A related phenomenon is where many people working independently have the same new idea at approximately the same time, and they publish in separate journals without knowledge of each other.
These are the reasons for publishing in a journal that is recognized as central to a specialty. If something is published on the internet in isolation, it's difficult to receive the attention of peers. The flip side is there may be considerable delay to publication in an active journal with a waiting list. |
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This "theorem" about these patterns of powers of two. The proof was never published in a well-reviewed journal, this is the only place where I have looked it up and found it. Maybe someone needs to publish it so it can be a more widely recognized phenomenon.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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This "theorem" about these patterns of powers of two. The proof was never published in a well-reviewed journal, this is the only place where I have looked it up and found it. Maybe someone needs to publish it so it can be a more widely recognized phenomenon.
While this is a nice result, and cool that you discovered it, this belongs to undergraduate university mathematics. It is not research-level math. Just saying, so nobody thinks it will be published in a research journal. The web page you found looks good. /JeppeSN |
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With the result shown for Mersenne primes earlier in the thread, let's create a divisibility test for 7.
A number divisible by 7 can be in the form 2^3n-1. -1 is equal to 3n+2 for n=-1. We can also now examine that numbers of the following types are divisible by 7 by adding 7 to the end of the yielded equations:
2^3n+6
2^3n+13
2^3n+20
And in the general case: 2^3n+(7n-1)
If we substitute a multiple of 7 into the equivalent side of the equation, we get:
7k=2^3n+(7n-1)
2^3=8, thus 2^3n=2^3^n=8^n.
8=1 mod 7, so the equation becomes congruent to 1+7n-1.
The 1's cancel leaving the true result 7k=7n mod 7.
Or a simpler version for computational purposes:
2^4+5=21
2^10+5=1029
2^4+26=42
2^10+26=1050.
With this we can find the equation 7k is always equivalent to 2^(6n+4)+3(7n+1)+2
7k=2^6n+4+3(7h+1)+2
2^6=64=1 mod 7
7k=2^4+3(7h+1)+2
7k-16=3(7h+1)+2
0=21h+3+2-7k+16
0=21h+5-7k+16
0=21h-7k+21. If all coefficients are divisible by 7, then the number is divisible by 7.
Example:
329=2^6n+4+3(7h+1)+2
329=1^n*16+3(7h+1)+2
329=16+3(7h+1)+2
313=3(7h+1)+2
313=21h+5
0=21h+308. If this is continually iterated you will find that 329 is a multiple of 7.
Iterate with 308:
308=2^6n+4+21h+5
308=16+21h+5
292=21h+5
0=21h-287.
287=16+21h+5
271=21h+5
266=21h
266=16+21h+5
250=21h+5
245=21h
245=21h+21
224=21h
224=21h+21
203=21h...
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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I have a PPS task (not mega) that was ran by my Pentium 32 bit CPU about a week ago and still hasn't been validated. And I noticed my wingman is using a GPU for this! How is he this slow?? Or is this task just queued for him later on.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Dave
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Sieve or LLR? No PPS LLR on GPUs. He may have a massive cache or be not active. How many does he have in work? Also it's holiday season so he may be offline. |
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LLR. He has like 4100 tasks on this one computer alone. His name is mofo22.
Work unit: http://www.primegrid.com/result.php?resultid=763050582
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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Crun-chiVolunteer tester
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You dont need to worry, deadline is 30 Dec 2016 | 20:59:53 UTC,after that time, server will resend task to first one computer that ask that type of task....
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92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie! |
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Michael GoetzVolunteer moderator
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I have a PPS task (not mega) that was ran by my Pentium 32 bit CPU about a week ago and still hasn't been validated. And I noticed my wingman is using a GPU for this! How is he this slow?? Or is this task just queued for him later on.
You are mistaken. There's no such thing as a PPS-LLR GPU task. (You can take my word as Gospel on this because I'm the one who installs the apps on the server.) Either this was w PPS-Sieve task (or some other GPU task), or whatever wingman task you're referring to is actually a CPU task.
That minor detail aside, as others have noted, there's many, many reasons why you'll need to wait for wingmen. On the longer tasks, with longer deadlines, it's not uncommon to wait for months until a task validates.
This is not a hobby well suited for the impatient. You will drive yourself crazy waiting for wingmen to return matching tasks. It's like watching paint dry -- except that paint dries a LOT faster! :)
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My lucky number is 75898524288+1 |
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Nvm. He aborted and it validated by Person 3 in about a half hour.
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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PRIME FOUND!!!!!
1146966*79^50005-1 is prime! (94897 digits)
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Nathan Hood, Amateur Mathematician
Favorite Number-53
1146966*79^50005-1 is prime! (94897 decimal digits, P = 3) Time : 2930.129 sec.
PRIMES AS DOUBLE CHECKER:
29320766^8192+1 is prime!
24526702^8192+1 is prime! |
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