(211117 - 1)/3581964369642\
70608221221853970927519972222557196875442622337153

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:(211117 - 1)/3581964369642\
70608221221853970927519972222557196875442622337153
Verification status (*):PRP
Official Comment (*):Mersenne cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c4 : Broadhurst, Primo
Decimal Digits:3284   (log10 is 3283.9963405349)
Rank (*):95414 (digit rank is 1)
Entrance Rank (*):65657
Currently on list? (*):no
Submitted:8/5/2011 18:25:27 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:101020
Status Flags:Verify
Score (*):28.982 (normalized score 0)

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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 702
Subcategory: "ECPP"
(archival tag id 213357, tag last modified 2024-03-24 06:37:14)
Mersenne cofactor (archivable *)
Prime on list: no, rank 38
Subcategory: "Mersenne cofactor"
(archival tag id 213358, tag last modified 2023-10-16 19:37:15)

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.

David Broadhurst writes (11 Sep 2014):  (report abuse)
certificate

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.
fieldvalue
prime_id101020
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/pfgw -o -f -q"(2^11117-1)/358196436964270608221221853970927519972222557196875442622337153" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] (2^11117-1)/3581....6875442622337153 1/1 mro=0 trial factoring to 858580 (2^11117-1)/3581964369...2622337153 has no small factor. [Elapsed time: 0.297 seconds]
modified2020-07-07 22:30:31
created2011-08-05 18:35:02
id131602

fieldvalue
prime_id101020
person_id9
machineRedHat Virtual STEM Server
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"(2^11117-1)/358196436964270608221221853970927519972222557196875442622337153" 2>&1 PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing (2^11117-1)/3581964369...2622337153 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 11, base 2+sqrt(11) Calling N-1 BLS with factored part 0.68% and helper 0.28% (2.32% proof) (2^11117-1)/3581964369...2622337153 is Fermat and Lucas PRP! (1.7706s+0.0082s) [Elapsed time: 2.00 seconds]
modified2020-07-07 22:30:31
created2011-08-05 18:36:06
id131609

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.