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: 25900+469721940591 Verification status (*): PRP Official Comment: Consecutive primes arithmetic progression (4,d=2880), ECPP Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): c45 : DavisK, NewPGen, Primo Decimal Digits: 1777   (log10 is 1776.0769744175) Rank (*): 64776 (digit rank is 4) Entrance Rank (*): 57101 Currently on list? (*): short Submitted: 11/12/2007 05:49:11 CDT Last modified: 11/12/2007 08:20:20 CDT Database id: 82959 Status Flags: Verify Score (*): 27.0667 (normalized score 0)

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.

Arithmetic Progressions of Primes (archivable class *)

Prime on list: no, rank 39, weight 35.7537585806825
Subcategory: "Arithmetic progression (4,d=*)"
(archival tag id 185914, tag last modified 2009-07-14 10:40:20)

Consecutive Primes in Arithmetic Progression (archivable class *)

Prime on list: yes, rank 1
Subcategory: "Consecutive primes in arithmetic progression (4,d=*)"
(archival tag id 185913, tag last modified 2007-11-12 08:20:20)

Elliptic Curve Primality Proof (archivable *)

Prime on list: no, rank 373
Subcategory: "ECPP"
(archival tag id 185915, tag last modified 2009-11-22 06:50:29)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Ken Davis writes (16 Jan 2008): 

The file http://www.geocities.com/kradenken/mfdata/cpap4.zip contains 4 directories (one for each prime in the CPAP) with the primo proofs/ validation etc in them.

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 82959 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 1 2 5900 469721940591 2>&1 [Ellapsed time: 7.040 seconds] modified 2008-01-03 10:54:43 created 2007-11-12 05:52:33 id 95032

field value prime_id 82959 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -tc -q"2^5900+469721940591" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2^5900+469721940591 [N-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(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) Reduced from FFT(768,18) to FFT(768,17) Reduced from FFT(768,17) to FFT(768,16) 11810 bit request FFT size=(768,16) Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) Reduced from FFT(768,18) to FFT(768,17) Reduced from FFT(768,17) to FFT(768,16) 11810 bit request FFT size=(768,16) Running N-1 test using base 11 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) Reduced from FFT(768,18) to FFT(768,17) Reduced from FFT(768,17) to FFT(768,16) 11810 bit request FFT size=(768,16) Running N-1 test using base 17 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) Reduced from FFT(768,18) to FFT(768,17) Reduced from FFT(768,17) to FFT(768,16) 11810 bit request FFT size=(768,16) Running N-1 test using base 19 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) Reduced from FFT(768,18) to FFT(768,17) Reduced from FFT(768,17) to FFT(768,16) 11810 bit request FFT size=(768,16) Running N+1 test using discriminant 31, base 1+sqrt(31) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) Reduced from FFT(768,18) to FFT(768,17) Reduced from FFT(768,17) to FFT(768,16) 11818 bit request FFT size=(768,16) Calling N+1 BLS with factored part 0.53% and helper 0.12% (1.71% proof) 2^5900+469721940591 is Fermat and Lucas PRP! (2.1900s+0.0000s) [Elapsed time: 2.00 seconds] modified 2008-01-03 10:54:43 created 2007-11-12 06:11:39 id 95036