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: 18672891658 · 4099#+1591789579 Verification status (*): PRP Official Comment: ECPP, consecutive primes arithmetic progression (4,d=210) Proof-code(s): (*): c14 : Fougeron, Primo Decimal Digits: 1763   (log10 is 1762.96448517) Rank (*): 64842 (digit rank is 1) Entrance Rank (*): 42101 Currently on list? (*): short Submitted: 10/30/2003 12:48:05 CDT Last modified: 10/30/2003 12:48:05 CDT Database id: 66904 Status Flags: Verify Score (*): 27.0436 (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 40, weight 35.7232262180482
Subcategory: "Arithmetic progression (4,d=*)"
(archival tag id 185107, tag last modified 2009-07-14 10:40:20)

Consecutive Primes in Arithmetic Progression (archivable class *)

Prime on list: yes, rank 2
Subcategory: "Consecutive primes in arithmetic progression (4,d=*)"
(archival tag id 185106, tag last modified 2007-11-12 05:50:20)

Elliptic Curve Primality Proof (archivable *)

Prime on list: no, rank 388
Subcategory: "ECPP"
(archival tag id 185108, tag last modified 2009-11-22 06:50:29)

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 66904 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"18672891658*4099#+1591789579" 2>&1 PFGW Version 20030811.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 435393 Running N-1 test using base 3 Primality testing 18672891658*4099#+1591789579 [N-1/N+1, Brillhart-Lehmer-Selfridge] 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) 11722 bit request FFT size=(768,16) Running N+1 test using discriminant 7, base 10+sqrt(7) 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) 11730 bit request FFT size=(768,16) Calling N+1 BLS with factored part 0.56% and helper 0.07% (1.78% proof) 18672891658*4099#+1591789579 is Fermat and Lucas PRP! (3.4761s+0.0006s) modified 2003-11-14 15:11:18 created 2003-10-30 12:53:01 id 71822