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: 9409 · 2522858 + 1 Verification status (*): Proven Official Comment: Generalized Fermat Proof-code(s): (*): L1204 : Brown1, PSieve, Srsieve, PrimeGrid, LLR Decimal Digits: 157400   (log10 is 157399.91501635) Rank (*): 33187 (digit rank is 1) Entrance Rank (*): 4777 Currently on list? (*): no Submitted: 7/9/2010 09:56:35 CDT Last modified: 7/9/2010 19:50:33 CDT Removed (*): 7/26/2010 11:28:43 CDT Database id: 93482 Status Flags: none Score (*): 40.9512 (normalized score 0.0413)

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 1426
Subcategory: "Generalized Fermat"
(archival tag id 210724, tag last modified 2020-02-22 14:50:24)

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 93482 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 9409 2 522858 1 2>&1 [Elapsed time: 9.755 seconds] modified 2011-12-27 16:48:39 created 2010-07-09 10:05:12 id 116328

field value prime_id 93482 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"9409*2^522858+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 9409*2^522858+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 1045752 bit request FFT size=(65536,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 9409*2^522858+1 is prime! (1420.2300s+0.0000s) [Elapsed time: 23.83 minutes] modified 2010-10-13 12:41:37 created 2010-07-09 19:04:11 id 116367