- 10365630 · Bern(3100)/(140592076277 · 66260150981141825531862457 · 179307479508256366206520177467103)

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: - 10365630 · Bern(3100)/(140592076277 · 66260150981141825531862457 · 179307479508256366206520177467103)
Verification status (*):PRP
Official Comment (*):Irregular ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c63 : Ritschel, TOPS, Primo
Decimal Digits:6943   (log10 is 6942.7893615584)
Rank (*):86276 (digit rank is 1)
Entrance Rank (*):75577
Currently on list? (*):short
Submitted:9/25/2016 09:05:08 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:122252
Status Flags:Verify
Score (*):31.3084 (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.
Irregular Primes (archivable *)
Prime on list: yes, rank 13
Subcategory: "Irregular Primes"
(archival tag id 218429, tag last modified 2023-03-11 16:02:31)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 433
Subcategory: "ECPP"
(archival tag id 218430, tag last modified 2023-10-03 00:37:15)

User comments about this prime (disclaimer):

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Thomas Ritschel writes (25 Sep 2016):  (report abuse)
Certificate available from here.

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.
machineUsing: Xeon 4c+4c 3.5GHz
notesPFGW Version [GWNUM 27.11] Primality testing 6156892324...4605747363 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 3 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N-1 BLS with factored part 0.34% and helper 0.08% (1.12% proof) 6156892324...4605747363 is Fermat and Lucas PRP! (4.5825s+0.0020s) [Elapsed time: 4.00 seconds]
modified2020-07-07 22:30:16
created2016-09-25 09:11:04

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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