531631540026641 · 61285077 + 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:531631540026641 · 61285077 + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L3494 : Batalov, NewPGen, LLR
Decimal Digits:999999   (log10 is 999999)
Rank (*):2719 (digit rank is 3)
Entrance Rank (*):1096
Currently on list? (*):short
Submitted:8/24/2021 04:38:35 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:132642
Status Flags:none
Score (*):46.633 (normalized score 5.0237)

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.

Serge Batalov writes (10 Sep 2021):  (report abuse)
Currently, the 3rd largest known proven under-one-million-decimal digit prime.
See also its sibling - the smallest known proven one-million-decimal digit prime.

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 -t -q"531631540026641*6^1285077+1" 2>&1 PFGW Version [GWNUM 29.8] Primality testing 531631540026641*6^1285077+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 61.31% 531631540026641*6^1285077+1 is prime! (32680.3529s+0.0077s) [Elapsed time: 9.08 hours]
modified2022-07-11 18:21:46
created2021-08-24 04:41:01

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