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drummers-lowrise
1) Message boards : Number crunching : Good Riddance 2020! Challenge (Message 147623)
Posted 5 hours ago by Profile JeppeSNProject donor
Yes, and Scott Brown has one, too. Can be seen on https://primes.utm.edu/primes/search.php?MaxAge=3&OnList=all&Number=200&Style=HTML. The primes with details are going to be visible on https://www.primegrid.com/primes/primes.php?project=DIV&factors=XGF&sortby=date when they have been validated on Top 5000. /JeppeSN

As discussed on Discord, there is an even more amazing one in the pipeline. Can be seen now by following the first link above (and will appear on the second link soon). Again tng, and this time it earns him an badge! /JeppeSN
2) Message boards : Fermat Divisor Search : Currently known Fermat divisors, sorted by k (Message 147619)
Posted 6 hours ago by Profile JeppeSNProject donor
Update: tng found one and got an F badge: 27*2^7963247 + 1 divides F(7963245). The new term is also underlined below.

Congratulations, tng! To appear on https://www.primegrid.com/primes/primes.php?project=ALL&factors=F&only=ONLY


k: (all known n that make k*2^n+1 a Fermat divisor)

--

3: 41, 209, 157169, 213321, 303093, 382449, 2145353, 2478785

5: 7, 25, 39, 75, 127, 1947, 3313, 23473, 125413

7: 14, 120, 290, 320, 95330, 2167800, [...?], 18233956

9: 67, 9431, 461081, 2543551

11: 18759, 960901

13: 20, 114296, 5523860

15: 229

17: 147, 747, 6539

19: 6838, 9450, 23290

21: 41, 276, 94801

23:

25: 2141884

27: 455, 672007, 7963247

29: 57, 231, 2027, 4727

31:

33: 18766

35:

37: 16

39: 13, 113549

41:

43:

45:

47:

49:

/JeppeSN
3) Message boards : Number crunching : Good Riddance 2020! Challenge (Message 147602)
Posted 21 hours ago by Profile JeppeSNProject donor
Yes, and Scott Brown has one, too. Can be seen on https://primes.utm.edu/primes/search.php?MaxAge=3&OnList=all&Number=200&Style=HTML. The primes with details are going to be visible on https://www.primegrid.com/primes/primes.php?project=DIV&factors=XGF&sortby=date when they have been validated on Top 5000. /JeppeSN
4) Message boards : Number crunching : Good Riddance 2020! Challenge (Message 147550)
Posted 2 days ago by Profile JeppeSNProject donor
The new multi-threading system is now live. Click here to set the maximum number of threads.

Is the "here" link safe to use, given that it contains a fixed time stamp tnow=1595298865 and some kind of fixed token ttok=78887263307c0cc2e93f633c9a9953d4? And it points to the "home" venue, not to the "primary (default)" venue. /JeppeSN
5) Message boards : Number crunching : Good Riddance 2020! Challenge (Message 147549)
Posted 2 days ago by Profile JeppeSNProject donor
and did not change the app_config to use 4 core per task.

You know you can set "Multi-threading: Max # of threads for each task" on https://www.primegrid.com/prefs.php?subset=project as described above? /JeppeSN
6) Message boards : Number crunching : New warnings when LLR2 detects Gerbicz errors (Message 147521)
Posted 3 days ago by Profile JeppeSNProject donor
It can happen that a computer runs correctly without any hardware errors for a long time, and then after that starts producing errors "by itself". As an example, if dust is gradually accumulating inside it, the cooling becomes less and less efficient, and at a certain point the computer will become too hot and start producing errors.

LLR2 is smart enough to see that the numbers do not make sense anymore, and will go back to the latest saved partial result and re-start from there. Because of that, LLR2 will still find the correct result eventually.

When the computer has hardware errors once in a while with LLR2, it can also have errors once in a while with other software on it. So it may be unstable (applications or the entire OS may crash from time to time, for example). Therefore you should try to fix it.

/JeppeSN
7) Message boards : General discussion : Suggestion: Team name in team 'info page' (Message 147512)
Posted 4 days ago by Profile JeppeSNProject donor
Easy one; it is in the URL preview when you hold the mouse pointer over "Free-DC".

/JeppeSN
8) Message boards : Number crunching : Good Riddance 2020! Challenge (Message 147506)
Posted 4 days ago by Profile JeppeSNProject donor
The largest known prime Fermat divisor is the megaprime 13 * 25523860+1, discovered by PrimeGrid this January, which divides F5523858 = 225523858+1. Will we break this record during the challenge?


Wrong. Likely copy-pasted from last years challenge when it was correct it had recently (19 days before the challenge) been correct. The largest known prime Fermat divisor (frozen archive version) is 7*218233956 + 1 found in October 2020 outside PrimeGrid. It is too huge (exponent near n=18.2M) to be beaten by the PPS-DIV project (sceduled to end at n=9M). /JeppeSN
9) Message boards : Wieferich and Wall-Sun-Sun Prime Search : WW project is live (Message 147399)
Posted 10 days ago by Profile JeppeSNProject donor
We are now past the region that was done in the WFS (Wieferich Search on PRPNet) project. So we are starting to see Wieferich instances on /stats_ww.php.

For primes, 2^(p-1) is congruent to 1 (mod p). In Wieferich, you consider the same expression modulo p^2 instead. Here on PrimeGrid, we stop at half the exponent, i.e. one squaring less.

So: 2^((p-1)/2)

Mod p, this 2^((p-1)/2) will be one of the square roots of 1. There are two square roots of 1 mod p, namely -1 and +1. By a result known as Second Supplement to Quadratic Reciprocity, it will be +1 if p is ±1 (mod 8), and it will be -1 if p is ±3 (mod 8). For example p=609757445465783651 found by Bloodnok. To do mod 8, we can consider only the last three digits 651. And 651 (=648+3) mod 8 is 3. So the base 2 is not a quadratic residue mod 609757445465783651 (the Legendre symbol is -1), and then:

2^(609757445465783650/2) is -1 (mod 609757445465783651)

Bloodnok's discovery:

2^(609757445465783650/2) is -1 +346*609757445465783651 (mod 609757445465783651^2)

/JeppeSN
10) Message boards : General discussion : Why does p divide 2^(p-1)-1? (Message 147382)
Posted 11 days ago by Profile JeppeSNProject donor
Ok, thanks. I thought there might be an intuitive way to see why it is true.

My intuition might be different than yours because of my educational background (which is why I wrote that the group gives the intuition). /JeppeSN


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