1213266377 · 235000 + 4859

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.

This prime's information:

Description:1213266377 · 235000 + 4859
Verification status (*):PRP
Official Comment (*):ECPP, consecutive primes arithmetic progression (3,d=2430)
Proof-code(s): (*):c4 : Broadhurst, Primo
Decimal Digits:10546   (log10 is 10545.133804402)
Rank (*):82611 (digit rank is 1)
Entrance Rank (*):66294
Currently on list? (*):no
Submitted:3/19/2014 19:33:22 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:117449
Status Flags:Verify
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: no, rank 6
Subcategory: "Consecutive primes in arithmetic progression (3,d=*)"
(archival tag id 217645, tag last modified 2024-06-28 08:37:19)
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 140, weight 38.207574671209
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 217646, tag last modified 2024-06-28 08:37:18)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 297
Subcategory: "ECPP"
(archival tag id 217647, tag last modified 2024-07-11 00:37:12)

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"1213266377*2^35000+4859" 2>&1 PFGW Version [GWNUM 26.5] Primality testing 1213266377*2^35000+4859 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 11, base 2+sqrt(11) Calling N-1 BLS with factored part 0.15% and helper 0.07% (0.54% proof) 1213266377*2^35000+4859 is Fermat and Lucas PRP! (18.5811s+0.0003s) [Elapsed time: 19.00 seconds]
modified2020-07-07 22:30:17
created2014-03-19 19:38:20

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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