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Message boards : News : GFN-1048576 Mega Prime!

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Van ZimmermanProject donor
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Message 109834 - Posted: 2 Sep 2017 | 17:03:28 UTC
Last modified: 23 Sep 2017 | 11:58:42 UTC

On 29 August 2017, 14:15:23 UTC, PrimeGrid’s Generalized Fermat Prime Search found the Generalized Fermat mega prime:

919444^1048576+1

The prime is 6,253,210 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 1st for Generalized Fermat primes and 12th overall. This is the first Generalized Fermat prime found for n=20, the second-largest prime found by PrimeGrid, and the second-largest non-Mersenne prime.

The discovery was made by Sylvanus A. Zimmerman (Van Zimmerman) of the United States using a Nvidia GeForce GTX 1060 in an Intel(R) Xeon(R) E3-1225 v3 CPU at 3.20GHz with 8GB RAM, running Microsoft Windows 10 Professional Edition. This GPU took about 4 hours 43 minutes to probable prime (PRP) test with GeneferOCL4. Sylvanus is a member of the Aggie The Pew team.

The prime was verified on 22 September 2017, 04:45:25 by Brian Konie (ScubaSteve) of the United States using an Intel(R) Xeon(R) E5-2620 CPU @ 2.00GHz with 16GB RAM, running Linux. This CPU took about 22 days, 13 hours, 25 minutes to probable prime (PRP) test with Genefer.

The PRP was confirmed prime by an Intel(R) Core(TM) i7-7700K CPU @ 4.20GHz with 16GB RAM, running Microsoft Windows 10 Professional Edition. This computer took about 3 days, 23 hours, 53 minutes to complete the primality test using multithreaded LLR.

For more details, please see the official announcement.

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Message 109845 - Posted: 2 Sep 2017 | 19:32:30 UTC

Extends https://oeis.org/A056993 (posted).

Congratulations!

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Message 109848 - Posted: 2 Sep 2017 | 19:45:34 UTC - in response to Message 109845.

Extends https://oeis.org/A056993 (posted).

Congratulations!


Yeah, that is something we have waited for for a long time.

Of course, there is the theoretical possibility that this is not the smallest n=20 generalized Fermat prime. The minimal base still in progress with n=20 appears to be 880342.

I know the number of candidates between 880342 and 919444 which have not been double-checked (or even successfully checked just once?) must be small.

/JeppeSN

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Message 109861 - Posted: 2 Sep 2017 | 22:30:55 UTC - in response to Message 109848.

Wow. Congratulations!!
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Message 109926 - Posted: 4 Sep 2017 | 6:21:51 UTC

Congratilation, this is significant found.

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Message boards : News : GFN-1048576 Mega Prime!

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