39161#/2310 - 510478

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:39161#/2310 - 510478
Verification status (*):PRP
Official Comment (*):ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c35 : Cami, Primo
Decimal Digits:16901   (log10 is 16900.607099434)
Rank (*):75748 (digit rank is 1)
Entrance Rank (*):56656
Currently on list? (*):no
Submitted:4/12/2013 06:43:12 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:112815
Status Flags:Verify
Score (*):34.0653 (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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 130
Subcategory: "ECPP"
(archival tag id 216084, tag last modified 2024-03-24 06:37:14)

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.

Pierre Cami writes (11 Sep 2014):  (report abuse)
Proven with PRIMO. The certificate can be found at http://www.ellipsa.net

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.
fieldvalue
prime_id112815
person_id9
machineDitto P4 P4
whatprp
notesCommand: /home/ditto/client/pfgw -tc -q"39161#/2310-510478" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 39161#/2310-510478 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 1+sqrt(5) Calling N+1 BLS with factored part 0.06% and helper 0.04% (0.24% proof) 39161#/2310-510478 is Fermat and Lucas PRP! (215.0929s+0.0204s) [Elapsed time: 3.58 minutes]
modified2020-07-07 22:30:21
created2013-04-12 07:41:46
id155951

fieldvalue
prime_id112815
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/pfgw -o -f -q"39161#/2310-510478" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 39161#/2310-510478 1/1 mro=0 trial factoring to 5062385 39161#/2310-510478 has no small factor. [Elapsed time: 9.177 seconds]
modified2020-07-07 22:30:21
created2013-04-12 08:23:49
id155970

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