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: 1043085905 · 235000 + 18197 Verification status (*): PRP Official Comment: ECPP, consecutive primes arithmetic progression (3,d=18198) Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): c4 : Broadhurst, Primo Decimal Digits: 10546   (log10 is 10545.068168316) Rank (*): 74368 (digit rank is 4) Entrance Rank (*): 66090 Currently on list? (*): short Submitted: 2/21/2014 12:43:37 CDT Last modified: 2/21/2014 13:22:31 CDT Database id: 117242 Status Flags: Verify, TrialDiv Score (*): 32.6046 (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.

Consecutive Primes in Arithmetic Progression (archivable class *)

Prime on list: yes, rank 2
Subcategory: "Consecutive primes in arithmetic progression (3,d=*)"
(archival tag id 217621, tag last modified 2014-03-19 14:52:09)

Arithmetic Progressions of Primes (archivable class *)

Prime on list: no, rank 124, weight 38.2075522696631
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 217622, tag last modified 2019-07-04 05:50:22)

Elliptic Curve Primality Proof (archivable *)

Prime on list: no, rank 159
Subcategory: "ECPP"
(archival tag id 217623, tag last modified 2019-06-02 14:20:07)

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 (11 Sep 2014): 

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 117242 person_id 9 machine Ditto P4 P4 what prp notes Command: /home/ditto/client/pfgw -tc -q"1043085905*2^35000+18197" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 1043085905*2^35000+18197 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 5 Running N+1 test using discriminant 11, base 3+sqrt(11) Calling N+1 BLS with factored part 0.03% and helper 0.02% (0.11% proof) 1043085905*2^35000+18197 is Fermat and Lucas PRP! (31.1955s+0.0003s) [Elapsed time: 32.00 seconds] modified 2014-04-01 17:37:38 created 2014-02-21 13:08:31 id 162761