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: V(6661)/(20413264084399 · 254844997471 · 6472729219639 · 8036635984600095627961 · 64250170013936618067104660874142964379889) Verification status (*): PRP Official Comment: Lucas cofactor, ECPP Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): c8 : Water, Broadhurst, Primo Decimal Digits: 1292   (log10 is 1291.82644712) Rank (*): 70264 (digit rank is 4) Entrance Rank (*): 53401 Currently on list? (*): short Submitted: 2/21/2005 04:24:57 CDT Last modified: 2/21/2005 04:24:57 CDT Database id: 73501 Status Flags: Verify Score (*): 26.0727 (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.

Elliptic Curve Primality Proof (archivable *)

Prime on list: no, rank 459
Subcategory: "ECPP"
(archival tag id 180907, tag last modified 2009-11-22 06:50:29)

Lucas cofactor (archivable *)

Prime on list: yes, rank 20
Subcategory: "Lucas cofactor"
(archival tag id 180908, tag last modified 2006-06-20 02:51:35)

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 Nov 2005): 

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 73501 person_id 9 machine Linux P4 2.8GHz what prp notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing V(6661)/(20413264084399*254844997471*6472729219639*8036635984...0095627961*6425017001...2964379889) [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 309698 Running N-1 test using base 7 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) Reduced from FFT(512,18) to FFT(512,17) 8592 bit request FFT size=(512,17) Running N+1 test using discriminant 13, base 1+sqrt(13) 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) Reduced from FFT(512,18) to FFT(512,17) 8600 bit request FFT size=(512,17) Running N+1 test using discriminant 13, base 2+sqrt(13) 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) Reduced from FFT(512,18) to FFT(512,17) 8600 bit request FFT size=(512,17) Running N+1 test using discriminant 13, base 3+sqrt(13) 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) Reduced from FFT(512,18) to FFT(512,17) 8600 bit request FFT size=(512,17) Running N+1 test using discriminant 13, base 6+sqrt(13) 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) Reduced from FFT(512,18) to FFT(512,17) 8600 bit request FFT size=(512,17) Running N+1 test using discriminant 13, base 10+sqrt(13) 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) Reduced from FFT(512,18) to FFT(512,17) 8600 bit request FFT size=(512,17) Running N+1 test using discriminant 13, base 13+sqrt(13) 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) Reduced from FFT(512,18) to FFT(512,17) 8600 bit request FFT size=(512,17) Running N+1 test using discriminant 13, base 14+sqrt(13) 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) Reduced from FFT(512,18) to FFT(512,17) 8600 bit request FFT size=(512,17) Calling N-1 BLS with factored part 0.89% and helper 0.21% (2.91% proof) V(6661)/(20413264084399*254844997471*6472729219639*8036635984...0095627961*6425017001...2964379889) is Fermat and Lucas PRP! (15.7901s+0.0890s) modified 2005-02-21 07:19:44 created 2005-02-21 07:19:28 id 78517