620366307356565 · 2253824 - 1

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:620366307356565 · 2253824 - 1
Verification status (*):Proven
Official Comment (*):Sophie Germain (p)
Proof-code(s): (*):x24 : Jarai_Z, Farkas, Csajbok, Kasza, Jarai, Unknown
Decimal Digits:76424   (log10 is 76423.430267617)
Rank (*):54467 (digit rank is 4)
Entrance Rank (*):16127
Currently on list? (*):short
Submitted:11/2/2009 19:46:50 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:90711
Status Flags:none
Score (*):38.7256 (normalized score 0.0018)

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.
Sophie Germain (p) (archivable *)
Prime on list: yes, rank 7
Subcategory: "Sophie Germain (p)"
(archival tag id 210538, tag last modified 2024-05-06 21:37:14)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 620366307356565 2 253824 -1 2>&1 [Elapsed time: 9.202 seconds]
modified2020-07-07 22:30:37
created2009-11-02 19:48:11

machineDitto P4 P4
notesCommand: /home/ditto/client/llr.pl 620366307356565*2^253824-1 2>&1 Starting Lucas Lehmer Riesel prime test of 620366307356565*2^253824-1 Using Zero Padded IBDWT : Mersenne fftlen = 12288, Used fftlen = 24576 V1 = 11 ; Computing U0... V1 = 11 ; Computing U0...done. Starting Lucas-Lehmer loop... 620366307356565*2^253824-1 is prime! Time : 212.072 sec. [Elapsed time: 3.53 minutes]
modified2020-07-07 22:30:37
created2009-11-02 19:48:21

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