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 2020-01-23, 16:54 #287 Batalov     "Serge" Mar 2008 San Diego, Calif. 23×1,301 Posts We would be amiss to not notice this new find that has just shown on radars... 13 · 25523860 + 1 divides Fermat F(5523858) Congratulations to Scott and the numerous PrimeGrid miners!
2020-01-23, 17:39   #288
paulunderwood

Sep 2002
Database er0rr

7×13×53 Posts

Quote:
 Originally Posted by Batalov We would be amiss to not notice this new find that has just shown on radars... 13 · 25523860 + 1 divides Fermat F(5523858) Congratulations to Scott and the numerous PrimeGrid miners!
There is now no need to run a PRP/N-1 prime check on F(5523858)

Last fiddled with by paulunderwood on 2020-01-23 at 17:43

2020-01-24, 02:41   #289
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

287716 Posts

Quote:
 Originally Posted by paulunderwood There is now no need to run a PRP/N-1 prime check on F(5523858)
haha, that was a good one.

Congrats to the finder(s) !

 2020-01-24, 13:52 #290 JeppeSN     "Jeppe" Jan 2016 Denmark 3048 Posts Good old F(5523858): I always thought it would be composite, but I did not expect such a tiny prime divisor! /JeppeSN
 2020-01-24, 15:07 #291 Dr Sardonicus     Feb 2017 Nowhere 3·2,179 Posts Once upon a time, long long ago, I noted that if n > 2 and k < 2n+2 + 2, the fact that N = k*2n+2 + 1 divides Fn in and of itself proves N is prime. In the case at hand (n = 5523858), k = 13 satisfies this condition. Last fiddled with by Dr Sardonicus on 2020-01-24 at 15:08 Reason: Omit unnecessary words!
 2020-01-24, 20:35 #292 ET_ Banned     "Luigi" Aug 2002 Team Italia 4,871 Posts Any more infos about the discovery? like the surname of Scott, or the setup he used for the search, or the time he devoted to it? Luigi --- P.S. Dr. James Scott Brown. Last fiddled with by ET_ on 2020-01-24 at 20:47
2020-01-24, 20:45   #293
mathwiz

Mar 2019

397 Posts

Quote:
 Originally Posted by ET_ Any more infos about the discovery? like the surname of Scott, or the setup he used for the search, or the time he devoted to it? Luigi ---

2020-01-24, 22:40   #294
ATH
Einyen

Dec 2003
Denmark

27×33 Posts

Quote:
 Originally Posted by ET_ Any more infos about the discovery? like the surname of Scott, or the setup he used for the search, or the time he devoted to it?
His name is Scott Brown it seems:

https://www.primegrid.com/workunit.php?wuid=638323572

https://www.primegrid.com/show_user.php?userid=1178

 2020-01-24, 23:41 #295 JeppeSN     "Jeppe" Jan 2016 Denmark 3048 Posts It is the same Scott Brown who found another Fermat factor, 9*2^2543551+1, back in 2011, in a similar way. In PrimeGrid, the participants detect the primality (two persons do it concurrently, the one finishing first is declared the finder). Whether the new Proth prime divides any Fermat number (and/or generalized Fermat numbers with bases at most 12) is detected by PrimeGrid's server, not the participant's computer. The link posted by ATH shows the timing (primality was reported "22 Jan 2020 | 15:00:58 UTC") and some hardware ("Intel(R) Core(TM) i7-4790 CPU @ 3.60GHz [Family 6 Model 60 Stepping 3]"). The other participant was Stefan Larsson (returned "22 Jan 2020 | 15:11:39 UTC"). At some point PrimeGrid will publish an official announcement (PDF). This was PrimeGrid's first Fermat divisor in five years. They recently introduced a new subproject that focuses on Proth primes with low "k" (the odd multiplier) because that gives higher probability of Fermat divisors. This approach was recommended by Ravi Fernando and others. /JeppeSN
 2020-01-25, 14:28 #296 Dr Sardonicus     Feb 2017 Nowhere 3×2,179 Posts Just for fun, I looked for small prime factors of the numbers k*2^5523860 + 1, k = 1 to 12. For all but three of them, the smallest factor can be found mentally. For two of the remaining three, the smallest factor is still quite small. k = 1 p = 17 k = 2 p = 3 k = 3 p = 14270779 k = 4 p = 5 k = 5 p = 3 k = 7 p = 2625617 k = 8 p = 3 k = 9 p = 5 k = 10 p = 11 k = 11 p = 3 k = 12 p = 7 For the remaining value, 6*2^5523860 + 1, I didn't look far enough to find any factors, but I didn't look all that far. Has (as I suspect) someone already found a factor by trial division, or otherwise shown it to be composite?
 2020-01-25, 17:04 #297 JeppeSN     "Jeppe" Jan 2016 Denmark C416 Posts PrimeGrid's official announcement is here and can be found in this thread of theirs. /JeppeSN

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