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2020-01-25, 18:03   #298
JeppeSN

"Jeppe"
Jan 2016
Denmark

9B16 Posts

Quote:
 Originally Posted by Dr Sardonicus 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?
Yes, your number 3*2^5523861 + 1 is composite, because PrimeGrid has established the primality status of all numbers 3*2^n ± 1 for n up to over 15.5 million, see their page stats_321_llr. We do not have access to their data, but if we ask them, they can maybe tell us if this candidate was eliminated during sieving (they may have the prime factor then) or during primality testing and double checking (they may have the residue then). However, I guess it is of limited interest. /JeppeSN

2020-01-27, 14:30   #299
Dr Sardonicus

Feb 2017
Nowhere

22×5×173 Posts

3*2^5523861 + 1 is definitely composite. From the List of primes k*2n + 1 for k < 300 we have for k = 3,
Quote:
 3 1, 2, 5, 6, 8, 12, 18, 30, 36, 41, 66, 189, 201, 209, 276, 353, 408, 438, 534, 2208, 2816, 3168, 3189, 3912, 20909, 34350, 42294, 42665, 44685, 48150, 54792, 55182, 59973, 80190, 157169, 213321, 303093, 362765, 382449, 709968, 801978, 916773, 1832496, 2145353, 2291610, 2478785, 5082306, 7033641, 10829346 [14884000]
(The exponents in bold give factors of Fermat numbers.)

 2020-05-25, 12:37 #300 ET_ Banned     "Luigi" Aug 2002 Team Italia 2×2,383 Posts New fermat factor! May 22nd, 2020 New Fermat factor from FermatSearch! 47893 . 2134998+1 is a Factor of F134995!!! Gary Gostin discovered the second Fermat factor of this year! This was discovered on an AMD EPYC 7702P based server running a new version of pmfs that incorporates George Woltman's gwnum library. Congratulations to Gary from FermatSearch, for his 83rd factor, we now have 352 Fermat factors known!
2020-05-25, 13:36   #301
mathwiz

Mar 2019

3×29 Posts

Quote:
 Originally Posted by ET_ May 22nd, 2020 New Fermat factor from FermatSearch! 47893 . 2134998+1 is a Factor of F134995!!! Gary Gostin discovered the second Fermat factor of this year! This was discovered on an AMD EPYC 7702P based server running a new version of pmfs that incorporates George Woltman's gwnum library. Congratulations to Gary from FermatSearch, for his 83rd factor, we now have 352 Fermat factors known!
Awesome, congrats!!

Is the new pmfs version available somewhere, either as source or a compiled Linux binary?

2020-05-25, 14:09   #302
ET_
Banned

"Luigi"
Aug 2002
Team Italia

2×2,383 Posts

Quote:
 Originally Posted by mathwiz Awesome, congrats!! Is the new pmfs version available somewhere, either as source or a compiled Linux binary?
Not at the moment. It's still in development.
No plans for a public release, either.

 2020-06-30, 10:20 #303 ET_ Banned     "Luigi" Aug 2002 Team Italia 129E16 Posts New Fermat Factor! Just received this email: Code: Hello Luigi, I would like to report the following new Fermat factor: 171,369,935 * 2^11077 + 1 divides F11075 This was discovered today (June 29) running pmfs on an HPE Superdome X system. Congratulations Gary!!! Please note that due to a migration to upgrade the webserver I had to schedule to grant power, space and bandwidth to you all, migration happening between today and tomorrow, the FermatSearch.org site update will be delayed. Luigi Last fiddled with by ET_ on 2020-06-30 at 10:25

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