1043085905 · 235000 + 18197

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

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 (*):75547 (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 5
Subcategory: "Consecutive primes in arithmetic progression (3,d=*)"
(archival tag id 217621, tag last modified 2020-04-27 12:20:26)
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 129, weight 38.2075522696631
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 217622, tag last modified 2020-04-27 12:20:25)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 169
Subcategory: "ECPP"
(archival tag id 217623, tag last modified 2020-08-13 20:20:20)

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):  (report abuse)

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -tc -q"1043085905*2^35000+18197" 2>&1 PFGW Version [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]
modified2020-07-07 17:30:18
created2014-02-21 13:08:31

Query times: 0.0005 seconds to select prime, 0.0008 seconds to seek comments.
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