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: 197418203 · 225000+6089 Verification status (*): PRP Official Comment: ECPP, consecutive primes arithmetic progression (3,d=6090) Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): FE4 : Morain, Broadhurst, FastECPP, OpenPFGW Decimal Digits: 7535   (log10 is 7534.04527879) Rank (*): 46927 (digit rank is 6) Entrance Rank (*): 30347 Currently on list? (*): short Submitted: 2/26/2005 17:35:01 CDT Last modified: 2/26/2005 17:35:01 CDT Database id: 73546 Status Flags: Verify Score (*): 31.562 (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 25
Subcategory: "ECPP"
(archival tag id 194567, tag last modified 2009-07-28 23:20:23)

Arithmetic Progressions of Primes (archivable class *)

Prime on list: no, rank 87, weight 36.9968969433317
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 194566, tag last modified 2009-02-12 20:20:07)

Consecutive Primes in Arithmetic Progression (archivable class *)

Prime on list: yes, rank 1
Subcategory: "Consecutive primes in arithmetic progression (3,d=*)"
(archival tag id 194565, tag last modified 2009-02-12 20:01:27)

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 73546 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"197418203*2^25000+6089" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 197418203*2^25000+6089 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 2115178 Running N-1 test using base 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) 50064 bit request FFT size=(3072,17) 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(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) 50072 bit request FFT size=(3072,17) Calling N+1 BLS with factored part 0.19% and helper 0.02% (0.60% proof) 197418203*2^25000+6089 is Fermat and Lucas PRP! (98.5591s+0.0003s) modified 2005-03-29 11:22:33 created 2005-02-26 17:55:31 id 78564