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: 5583295473 · 280828-1 Verification status (*): Proven Official Comment: Twin (p) Proof-code(s): (*): g336 : Tornberg, PRP, NewPGen, Proth.exe Decimal Digits: 24342   (log10 is 24341.39938014) Rank (*): 33418 (digit rank is 3) Entrance Rank (*): 20079 Currently on list? (*): no Submitted: 1/22/2006 14:09:41 CDT Last modified: 1/22/2006 18:06:05 CDT Database id: 76823 Status Flags: none Score (*): 35.1937 (normalized score 0.0044)

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.

Twin Primes (archivable *)

Prime on list: no, rank 21
Subcategory: "Twin (p)"
(archival tag id 191889, tag last modified 2009-11-14 12:20:28)

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 76823 person_id 9 machine Linux P4 2.8GHz what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 5583295473 2 80828 -1 2>&1 [Elapsed time: 11.017 seconds] modified 2006-02-01 23:37:09 created 2006-01-22 14:22:00 id 82626

field value prime_id 76823 person_id 9 machine WinXP Pentium M 1.7GHz what prime notes Command: pfgw.exe -n -tp -q"5583295473*2^80828-1" 2>&1 Primality testing 5583295473*2^80828-1 [N+1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 99.96% 5583295473*2^80828-1 is prime! (433.1858s+0.3482s) PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Running N+1 test using discriminant 5, base 1+sqrt(5) [Elapsed time: 432 seconds] modified 2006-02-01 23:37:09 created 2006-01-22 15:30:38 id 82630