To be removed soon:   English

2^77232917 - 1

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 2
Subcategory: "Mersenne"
(archival tag id 218966, tag last modified 2018-12-21 09:15:32)

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 (3 Jan 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 50th Mersenne in terms of size. We will remove the question mark when GIMPS completes checking all lower exponents twice and comparing the residues.

Chris Caldwell writes (3 Jan 2018):  (report abuse)

The official credit line for this prime is "Pace, Woltman, Kurowski, Blosser & GIMPS" This prime was externally verified. From the press release: The primality proof took six days of non-stop computing on a PC with an Intel i5-6600 CPU. To prove there were no errors in the prime discovery process, the new prime was independently verified using four different programs on four different hardware configurations. Aaron Blosser verified it using Prime95 on an Intel Xeon server in 37 hours. David Stanfill verified it using gpuOwL on an AMD RX Vega 64 GPU in 34 hours. Andreas Höglund verified the prime using CUDALucas running on NVidia Titan Black GPU in 73 hours. Ernst Mayer also verified it using his own program Mlucas on 32-core Xeon server in 82 hours. Andreas Höglund also confirmed using Mlucas running on an Amazon AWS instance in 65 hours.

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.