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: primB(95655) Verification status (*): PRP Official Comment: Lucas Aurifeuillian primitive part, ECPP Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): c4 : Broadhurst, Primo Decimal Digits: 4564   (log10 is 4563.4208968925) Rank (*): 53220 (digit rank is 1) Entrance Rank (*): 50819 Currently on list? (*): short Submitted: 5/26/2009 15:24:49 CDT Last modified: 5/26/2009 15:50:24 CDT Database id: 88514 Status Flags: Verify Score (*): 30.0052 (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.

Lucas Aurifeuillian primitive part (archivable *)

Prime on list: yes, rank 3
Subcategory: "Lucas Aurifeuillian primitive part"
(archival tag id 210449, tag last modified 2009-06-28 19:50:24)

Elliptic Curve Primality Proof (archivable *)

Prime on list: no, rank 98
Subcategory: "ECPP"
(archival tag id 210450, tag last modified 2009-11-14 14:20:22)

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.

David Broadhurst writes (26 May 2009): 

certificate

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 88514 person_id 9 machine Ditto P4 P4 what trial_divided notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] 2635705558...3420796327.........3226552256385776 1/1 trial factoring to 1227979 2635705558...6516988481 has no small factor. [Ellapsed time: 2.507 seconds] modified 2009-05-30 11:45:28 created 2009-05-26 15:35:02 id 106391

field value prime_id 88514 person_id 9 machine Ditto P4 P4 what prp notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2635705558...6516988481 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1792,21) to FFT(1792,20) Reduced from FFT(1792,20) to FFT(1792,19) Reduced from FFT(1792,19) to FFT(1792,18) Reduced from FFT(1792,18) to FFT(1792,17) 30328 bit request FFT size=(1792,17) Running N-1 test using base 17 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1792,21) to FFT(1792,20) Reduced from FFT(1792,20) to FFT(1792,19) Reduced from FFT(1792,19) to FFT(1792,18) Reduced from FFT(1792,18) to FFT(1792,17) 30328 bit request FFT size=(1792,17) Running N-1 test using base 43 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1792,21) to FFT(1792,20) Reduced from FFT(1792,20) to FFT(1792,19) Reduced from FFT(1792,19) to FFT(1792,18) Reduced from FFT(1792,18) to FFT(1792,17) 30328 bit request FFT size=(1792,17) Running N+1 test using discriminant 61, base 3+sqrt(61) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1792,21) to FFT(1792,20) Reduced from FFT(1792,20) to FFT(1792,19) Reduced from FFT(1792,19) to FFT(1792,18) Reduced from FFT(1792,18) to FFT(1792,17) 30336 bit request FFT size=(1792,17) Calling N-1 BLS with factored part 1.62% and helper 0.12% (4.98% proof) 2635705558...6516988481 is Fermat and Lucas PRP! (12.0900s+0.0000s) [Elapsed time: 13.00 seconds] modified 2009-05-26 15:38:15 created 2009-05-26 15:38:02 id 106393