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: 23963+1031392866 Verification status (*): PRP Official Comment: Consecutive primes arithmetic progression (4,d=1500) Proof-code(s): (*): c32 : DavisK, OpenPFGW, Primo Decimal Digits: 1312   (log10 is 1311.34390608) Rank (*): 69306 (digit rank is 44) Entrance Rank (*): 54866 Currently on list? (*): short Submitted: 10/19/2005 05:27:55 CDT Last modified: 10/19/2005 06:04:58 CDT Database id: 75971 Status Flags: Verify Score (*): 26.1195 (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.

Consecutive Primes in Arithmetic Progression (archivable class *)

Prime on list: yes, rank 3
Subcategory: "Consecutive primes in arithmetic progression (4,d=*)"
(archival tag id 185196, tag last modified 2007-11-12 05:50:20)

Arithmetic Progressions of Primes (archivable class *)

Prime on list: no, rank 44, weight 34.5031811145119
Subcategory: "Arithmetic progression (4,d=*)"
(archival tag id 185197, tag last modified 2009-07-14 10:40:20)

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 75971 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"23^963+1031392866" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 23^963+1031392866 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 314847 Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(512,22) to FFT(512,21) Reduced from FFT(512,21) to FFT(512,20) Reduced from FFT(512,20) to FFT(512,19) Reduced from FFT(512,19) to FFT(512,18) 8722 bit request FFT size=(512,18) Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(512,22) to FFT(512,21) Reduced from FFT(512,21) to FFT(512,20) Reduced from FFT(512,20) to FFT(512,19) Reduced from FFT(512,19) to FFT(512,18) 8722 bit request FFT size=(512,18) Running N+1 test using discriminant 11, base 1+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(512,22) to FFT(512,21) Reduced from FFT(512,21) to FFT(512,20) Reduced from FFT(512,20) to FFT(512,19) Reduced from FFT(512,19) to FFT(512,18) 8730 bit request FFT size=(512,18) Calling N-1 BLS with factored part 0.28% and helper 0.14% (1.01% proof) 23^963+1031392866 is Fermat and Lucas PRP! (1.2405s+0.0003s) [Elapsed time: 2 seconds] modified 2005-10-19 12:27:07 created 2005-10-19 06:04:56 id 81166