1)
Message boards :
Number crunching :
Badges III
(Message 147261)
Posted 886 days ago by Ravi Fernando
Thanks to genefer 3.3.5 and the challenge:
 
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2)
Message boards :
Wieferich and Wall-Sun-Sun Prime Search :
New Version Testing
(Message 147181)
Posted 887 days ago by Ravi Fernando
I'll take Mac CPU multithreaded.
Done. All tests passed:
1 (18446744013709551615 18446744073709551615 -t 4):
no special instances
509DE6503B2A6E8E
2 (1 6e10 -t 4):
5255 special instances + 2 Wieferich primes
8B77D2DA053842DD
3 (227630e10 227636e10 -t 4):
2276306935816523 is a Wieferich special instance (-1 -3 p)
6522CBC4CA2E4CFF
4 (338772621946054253 338772681946054253 -t 4):
338772621946054253 is a WallSunSun special instance (+0 +91 p)
589A69274A6AB5A8
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3)
Message boards :
Wieferich and Wall-Sun-Sun Prime Search :
New Version Testing
(Message 147136)
Posted 888 days ago by Ravi Fernando
I'll take Mac CPU multithreaded.
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4)
Message boards :
Problems and Help :
Challenge Series - I'm never in
(Message 146914)
Posted 897 days ago by Ravi Fernando
For future reference, no registration is required, and there's no such thing as being "rejected" from a challenge. The most common problem that keeps people out of the challenge standings is that they download work before the challenge starts, either intentionally or because of their cache settings. In your case, I can see that you downloaded one GFN20 task about 45 minutes before the challenge started, and another about 10 minutes after it started. The first one won't count (even though you finished it during the challenge), but the second one does (but it didn't show up immediately in the stats because they're only generated every 15 minutes).
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5)
Message boards :
Proth Prime Search :
Can PPS-Mega be a Fermat Divisor?
(Message 146753)
Posted 901 days ago by Ravi Fernando
There are Fermat divisors whose existence seem greatly improbable, yet here they are:
1527888802614951 · 2120 + 1 divides F118
15249465809 · 22591 + 1 divides F2587
There are more with large k: Fermat factors
Or is that 1/k conjectured probability not true for small n?
The 1/k heuristic is fine in these cases; it's just that people have searched many billions of candidates, and a very large number of very small probabilities adds up to a reasonable probability. It's important here that the factors you're referring to are only tens to hundreds of digits long, so they can be tested millions of times faster than megaprimes.
(As an aside, the extremely low-n, high-k end of the FermatSearch spectrum doesn't even search one candidate at a time; they literally expand out the Fermat number and try to factor it with the elliptic curve method. That's how we know some Fermat divisors where k has ~50 digits.)
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6)
Message boards :
Proth Prime Search :
Can PPS-Mega be a Fermat Divisor?
(Message 146726)
Posted 901 days ago by Ravi Fernando
Yes. In fact the world record Fermat divisor before DIV was a PPS-Mega: 193*2^3329782+1.
It's less likely now, because PPS-Mega is searching 1200<k<10000 instead of k<1200, but it's still certainly possible. (Rule of thumb: if k*2^n+1 is prime where k is odd, it has a 1/k chance of being a Fermat divisor. There are rare examples of k's that break this rule, meaning they have either a better chance or no chance at all.) For what it's worth, I think DIV, PPS, PPSE, and 321 are currently all better bets.
Edit: oh wow, I'm slow.
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7)
Message boards :
Wieferich and Wall-Sun-Sun Prime Search :
Which near-finds are shown?
(Message 146684)
Posted 903 days ago by Ravi Fernando
I hope I didn't miss something obvious, but the results page now shows a prime found by Grzegorz with A = 193.
WW by the numbers says only primes with |A|<=100 are shown for the range covered by PRP previously. That prime is at 265E15, so below the previous limit of 6E17.
You did miss something: this is a near-Wall-Sun-Sun prime, not a near-Wieferich, and the PRPNet WSS search didn't get as far as the Wieferich search. In fact this prime is just beyond the PRPNet search limit.
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8)
Message boards :
General discussion :
Extended generalized Fermat prime?
(Message 146649)
Posted 904 days ago by Ravi Fernando
Not sure where you're getting the idea that none of them are known. There are plenty of small ones--see e.g. the table with "a" and "b" columns a little ways below here. But there are no proven xGFN primes that are large enough for Caldwell's list, simply because it's usually not feasible to factor p+1 or p-1. For example, the two PRPs of the form a^2^16 + b^2^16 listed here cannot be proved prime with current methods, even though they're pretty small by T5K standards.
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9)
Message boards :
Generalized Fermat Prime Search :
Genefer 3.3.5 testing
(Message 146636)
Posted 904 days ago by Ravi Fernando
I'm starting Mac avxi 19, which should take a day or two.
Done:
Command line: ./genefer_macintel64 -x avxi -q 3638450^524288+1
Low priority change succeeded.
Testing 3638450^524288+1...
Using avxi transform
Starting initialization...
Initialization complete (2.245 seconds).
Estimated time for 3638450^524288+1 is 28:50:00
3638450^524288+1 is a probable prime. (3439810 digits) (err = 0.0039) (time = 30:03:53) 18:00:23
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10)
Message boards :
Generalized Fermat Prime Search :
Genefer 3.3.5 testing
(Message 146610)
Posted 906 days ago by Ravi Fernando
I'm starting Mac avxi 19, which should take a day or two.
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