New Fermat factors

[JeppeSN]

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

[Dr Sardonicus]

3*2^5523861 + 1 is definitely composite. From the List of primes k*2ⁿ + 1 for k < 300 we have for k = 3,

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.)

[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!

[mathwiz]

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?

[ET_]

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.

[ET_]

Just received this email:

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

[ryanp]

From my recent Proth prime:

7*2^18233956+1 is a Factor of F18233954!!!! (163569.267086 seconds)

[Gary]

Originally Posted by ryanp

From my recent Proth prime:

7*2^18233956+1 is a Factor of F18233954!!!! (163569.267086 seconds)

Congrats Ryan!!!!!!!!!! That is one HUGE factor.

[carpetpool]

Originally Posted by ryanp

From my recent Proth prime:

7*2^18233956+1 is a Factor of F18233954!!!! (163569.267086 seconds)

Congrats on a World Record Fermat Divisor!



_{PrimeGrid has held the record for many years up until now...}

Way to go!

[ET_]

Originally Posted by ryanp

From my recent Proth prime:

7*2^18233956+1 is a Factor of F18233954!!!! (163569.267086 seconds)

Congratulations! Did you find it on ProthSearch?
Any more infos related to the computing system and the program you used (and its maintainer)?

Luigi
---

[Dr Sardonicus]

Originally Posted by ryanp

From my recent Proth prime:

7*2^18233956+1 is a Factor of F18233954!!!! (163569.267086 seconds)

Great -- another proof that the number is prime! Congratulations!