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drummers-lowrise
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11)
Message boards :
Project Staging Area :
New Factorial prime
(Message 153190)
Posted 625 days ago by  Bur
When I saw this I was excited at first, but seeing how it's that close to PRPnet's wavefront makes me a bit suspicious...
https://primes.utm.edu/primes/page.php?id=133139
Of course Factorial primes aren't exclusive to PRPnet, but it still makes a not-so-good impression.
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12)
Message boards :
Wieferich and Wall-Sun-Sun Prime Search :
Ratio between near-WW primes
(Message 153161)
Posted 626 days ago by Bur
Update 10-01-2022
Tests upper bound: 10.2e18 / 18e18 (55 %, +0 %)
Number of near-WW found: 311 (+-1)
Distribution:
|A|<= | Actual | Expected | Deviation
-------|--------|----------|-----------
1000 | 311 | - | -
100 | 34 | 31 | +10 %
10 | 2 | 3 | -33 %
0 | 0 | 0 | 0 %
Based on the current number of near-WW
found, the probability for a WW prime is:
16 % (+ 1%).
At 18e18 we would reach:
28 % (-0 %)
100 % would be reached at:
66e18 (+1e18)
Last week average numbers tested per day:
1.41E16 (+- N/A)
ETA project completion:
582 days (+- N/A)
Things are still slow, last week's average is 9400 completed tasks/day. Due to DC that corresponds to 14E16 numbers checked / day. At that rate it'll be 582 days to complete the project. I added that to the stats.
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13)
Message boards :
Wieferich and Wall-Sun-Sun Prime Search :
Ratio between near-WW primes
(Message 153038)
Posted 632 days ago by Bur
Update 03-01-2022
Last update ist two weeks back, so mind that when looking at the differences. And we reached 1e19. Only 8 quintillion numbers left!
Tests upper bound: 10.1E18 / 18E18 (55 %, +1 %)
Number of near-WW found: 310 (+-2)
Distribution:
|A|<= | Actual | Expected | Deviation
-------|--------|----------|-----------
1000 | 310 | - | -
100 | 34 | 31 | +10 %
10 | 2 | 3 | -33 %
0 | 0 | 0 | 0 %
Based on the current number of near-WW
found, the probability for a WW prime is:
16 % (+ 1%).
At 18e18 we would reach:
28 % (-1 %)
100 % would be reached at:
65E18 (+1E18)
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14)
Message boards :
Number crunching :
Badges III
(Message 153037)
Posted 632 days ago by Bur
First LLR turquoise!
I'll keep going though until I finally find a Proth prime. It's expected to happen once in about 30,000 tests and I'm at 24,500 which corresponds to 3 weeks of additional work.
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15)
Message boards :
General discussion :
Implementing an Algorithm?
(Message 153018)
Posted 633 days ago by Bur
You can write a simple Pari GP program:
for (k=1, oo, n=3^k+2; if (Mod(2, n)^((n-1)/2) == -1, print(k); if (!ispseudoprime(n), print("Failed!"))));
The test checks if n is an Euler–Jacobi pseudoprime. So this first checks whether n is prime under the assumption that the conjecture is true and then, additionally, does a PRP test as a means to potentially disprove the conjecture?
Because 3^k + 2 increases exponentially, if n is a PRP then it is most likely prime. Why is that? Couldn't any number be written as 3^k + m and thus increase exponentially with increasing k?
Is the test for primality under the assumption of the conjecture to be true computationally faster than a PRP test? If so, it could be an interesting way to generate large PRPs.
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16)
Message boards :
Generalized Fermat Prime Search :
Guess the number of digits in the LAST GFN-17-LOW prime
(Message 152968)
Posted 634 days ago by Bur
999,909 digits.
Should correspond to a base between 42518334 and 42519078. If my PARI game isn't way off.
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17)
Message boards :
Number crunching :
Sabotage of Number Crunching
(Message 152964)
Posted 634 days ago by Bur
And Mr Wunk never noticed he had zero successful WUs? Or at least that his score didn't increase?
Nice to know it's finally solved... :D
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18)
Message boards :
General discussion :
Get prime from concatenating first n numbers
(Message 152778)
Posted 643 days ago by Bur
Ah, I had read ?logint but didn't see why it could be used at first.
So the output of logint(a,b) is always identical to floor(log_b(a)) it just saves computing time by not going through the actual calculation of the log?
Interesting take on the & instead of if. Now I realized I actually used that a couple of times before just not in such simple constructs but only within an if clause to indicate progress by throwing an &!(print(...)) in there. Btw, is it convention that print(a) returns 0 upon successfully printing?
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19)
Message boards :
Extended Sierpinski Problem :
k = 202705
(Message 152776)
Posted 644 days ago by Bur
If I'm not wrong and also assuming a sieving percentage of 1%, about 23000 tests are required to produce a mega prime.
1% sounds a bit optimistic to me. My rule of thumb is that the number of tasks needed to find a prime is roughly #(digits)/30.
That would correspond to a sieving rate of about 1.4%?
Btw, I was looking at the stats and saw that the number of workunits per 1M range of k for Woodall numbers decreases steadily with increasing k. For example 1M < k < 2M there were 36000 workunits and for 18M < k < 19M there were only 28000. Cullen shows a similar trend, but way less pronounced.
Were the larger numbers sieved more deeply or is there another reason?
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20)
Message boards :
General discussion :
Get prime from concatenating first n numbers
(Message 152773)
Posted 644 days ago by Bur
Jeppe, I tried the same, but my code for creating the number is a bit more complicated... :)
m=2000;p=0;k=0;for (i=1,m,k+=ceil(log(i)/log(10));p+=i*10^k;if(ispseudoprime(p),print("Prime: ",p)))
And the other suggested format of increasing and then decreasing values like 12345678910987654321:
updown(r,s) = {
b=s;
for(a=r,s-1,
p=0;k=0;for (i=a,b,p+=i*10^k;k+=(floor(log(i)/log(10))+1));
q=0;k=0;for (i=1,b-a,j=b-i;q+=j*10^k;k+=(floor(log(j)/log(10))+1));
p+=q*10^(floor(log(p)/log(10))+1);
\\ print(p);
if(ispseudoprime(p),print("yay: ",p," is prime!"))
)
}
And to run it: for(i=2,100,updown(1,i)) tests all number with 2 ... 100 in the middle and beginning at 1 to the middle value. Such as 121, 232, 12321, 343, 23432, 1234321, ...
Your slim code could be used there as well though. I got to understand what's going on there at first though.
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