282589933 - 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:282589933 - 1
Verification status (*):External
Official Comment (*):Mersenne 51??
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):G16 : Laroche, GIMPS, Prime95
Decimal Digits:24862048   (log10 is 24862047.172879)
Rank (*):1 (digit rank is 1)
Entrance Rank (*):1
Currently on list? (*):short
Submitted:12/21/2018 14:57:42 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:125874
Status Flags:Verify
Score (*):56.4713 (normalized score 95768.3569)

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.
Mersenne (archivable *)
Prime on list: yes, rank 1
Subcategory: "Mersenne"
(archival tag id 220011, tag last modified 2023-03-11 15:53:59)

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.

Chris Caldwell writes (9 Jun 2020):  (report abuse)

The official credit line for this prime is "P. Laroche, G. Woltman, A. Blosser, et al." This prime was externally verified. The primality proof took twelve days of non-stop computing on a machine with an Intel i5-4590T CPU. To prove there were no errors in the prime discovery process, the new prime was independently verified using three different programs on three different hardware configurations. See the press release:

  • Andreas Höglund verified the prime using CUDALucas running on a NVidia V100 GPU in 21 hours.
  • Andreas Höglund also verified the prime using Mlucas running on 16 cores of an Amazon AWS instance in 72 hours.
  • Aaron Blosser also verified it using Prime95 on an Intel 7700K processor in 6 days, 8 hours.

Chris Caldwell writes (21 Dec 2018):  (report abuse)
Not every Mersenne number less than this one has been checked even once for primality by GIMPS, so it is unknown if this is the 51st Mersenne in terms of size. We will remove the question mark when GIMPS completes checking all lower exponents twice and comparing the residues.

Verification data:

Some of the very largest primes are externally verified by trusted groups or individuals and we do not reverify them at this site. This is one of those.
Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
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