At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

This prime's information:

field (help) value Description: 346762232768 + 1 Verification status (*): Proven Official Comment: Generalized Fermat Proof-code(s): (*): p316 : Yama, GeneFer, AthGFNSieve, PrimeGrid, OpenPFGW Decimal Digits: 214304   (log10 is 214303.76037182) Rank (*): 22345 (digit rank is 1) Entrance Rank (*): 2010 Currently on list? (*): no Submitted: 1/20/2011 04:43:33 CDT Last modified: 2/13/2011 12:14:57 CDT Removed (*): 2/26/2012 12:15:11 CDT Database id: 97524 Status Flags: none Score (*): 41.9008 (normalized score 0.1143)

Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper.  Such primes are tracked with archival tags.

Generalized Fermat (archivable *)

Prime on list: no, rank 1111
Subcategory: "Generalized Fermat"
(archival tag id 213093, tag last modified 2019-12-04 09:50:21)

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions.  We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.

field value prime_id 97524 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 1 3467622 32768 1 2>&1 [Elapsed time: 8.191 seconds] modified 2011-12-27 16:48:35 created 2011-01-20 04:48:09 id 124438

field value prime_id 97524 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -t -q"3467622^32768+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 3467622^32768+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(98304,20) to FFT(98304,19) Reduced from FFT(98304,19) to FFT(98304,18) Reduced from FFT(98304,18) to FFT(98304,17) Reduced from FFT(98304,17) to FFT(98304,16) 1423812 bit request FFT size=(98304,16) Calling Brillhart-Lehmer-Selfridge with factored part 88.10% 3467622^32768+1 is prime! (-287.0246s+0.0500s) [Elapsed time: 2.59 hours] modified 2011-03-25 10:27:31 created 2011-01-20 05:08:01 id 124440