4158932595 · 2143074 - 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:4158932595 · 2143074 - 1
Verification status (*):Proven
Official Comment (*):Sophie Germain (2p+1)
Proof-code(s): (*):L3494 : Batalov, NewPGen, LLR
Decimal Digits:43080   (log10 is 43079.18458151)
Rank (*):62125 (digit rank is 1)
Entrance Rank (*):55524
Currently on list? (*):no
Submitted:7/6/2019 16:32:39 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:126618
Status Flags:none
Score (*):36.9572 (normalized score 0.0003)

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 (2p+1) (archivable *)
Prime on list: no, rank 26
Subcategory: "Sophie Germain (2p+1)"
(archival tag id 220339, tag last modified 2023-11-19 12:37:21)

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 (pool) 4c+4c 3.5GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tp -q"4158932595*2^143074-1" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 4158932595*2^143074-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Calling Brillhart-Lehmer-Selfridge with factored part 99.98% 4158932595*2^143074-1 is prime! (34.8192s+0.0001s) [Elapsed time: 34.00 seconds]
modified2020-07-07 22:30:13
created2019-07-06 16:33:37

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