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: 87 · 224582+2579 Verification status (*): PRP Official Comment: ECPP, consecutive primes arithmetic progression (3,d=1290) Proof-code(s): (*): c31 : Andersen, Alm, Rosenthal, OpenPFGW, Primo Decimal Digits: 7402   (log10 is 7401.85887266) Rank (*): 47096 (digit rank is 1) Entrance Rank (*): 29469 Currently on list? (*): short Submitted: 11/19/2004 09:21:34 CDT Last modified: 11/19/2004 09:21:34 CDT Database id: 72428 Status Flags: Verify Score (*): 31.5071 (normalized score 0.0001)

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.

Elliptic Curve Primality Proof (archivable *)

Prime on list: no, rank 29
Subcategory: "ECPP"
(archival tag id 194607, tag last modified 2009-08-18 08:20:24)

Arithmetic Progressions of Primes (archivable class *)

Prime on list: no, rank 89, weight 36.9331285714345
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 194606, tag last modified 2009-02-12 20:20:07)

Consecutive Primes in Arithmetic Progression (archivable class *)

Prime on list: yes, rank 2
Subcategory: "Consecutive primes in arithmetic progression (3,d=*)"
(archival tag id 194605, tag last modified 2009-02-12 20:01:27)

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 72428 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"87*2^24582+2579" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 87*2^24582+2579 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 2075030 Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3072,21) to FFT(3072,20) Reduced from FFT(3072,20) to FFT(3072,19) Reduced from FFT(3072,19) to FFT(3072,18) Reduced from FFT(3072,18) to FFT(3072,17) 49186 bit request FFT size=(3072,17) Running N+1 test using discriminant 5, base 1+sqrt(5) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3072,21) to FFT(3072,20) Reduced from FFT(3072,20) to FFT(3072,19) Reduced from FFT(3072,19) to FFT(3072,18) Reduced from FFT(3072,18) to FFT(3072,17) 49194 bit request FFT size=(3072,17) Calling N+1 BLS with factored part 0.09% and helper 0.02% (0.30% proof) 87*2^24582+2579 is Fermat and Lucas PRP! (32.0126s+0.0003s) modified 2004-11-20 19:47:49 created 2004-11-19 09:23:33 id 77426