(212451 - 1)/87065160674565854360715728029229940740377

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:(212451 - 1)/87065160674565854360715728029229940740377
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:3708   (log10 is 3707.1846316064)
Rank (*):93959 (digit rank is 1)
Entrance Rank (*):49451
Currently on list? (*):no
Submitted:10/9/2008 20:20:52 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:85612
Status Flags:Verify
Score (*):29.3591 (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 664
Subcategory: "ECPP"
(archival tag id 186346, tag last modified 2024-03-24 06:37:14)
Mersenne cofactor (archivable *)
Prime on list: no, rank 36
Subcategory: "Mersenne cofactor"
(archival tag id 186347, 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_id85612
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"(2^12451-1)/(4980401*15289230353*1143390212315192593598809)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] (2^12451-1)/(4980401*1528.........1433902123151925 1/1 trial factoring to 979687 (2^12451-1)/(4980401*15289230353*1143390212...2593598809) has no small factor. [Elapsed time: 0.370 seconds]
modified2020-07-07 22:30:39
created2008-10-09 20:22:01
id100695

fieldvalue
prime_id85612
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"(2^12451-1)/(4980401*15289230353*1143390212315192593598809)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (2^12451-1)/(4980401*15289230353*1143390212...2593598809) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1536,21) to FFT(1536,20) Reduced from FFT(1536,20) to FFT(1536,19) Reduced from FFT(1536,19) to FFT(1536,18) Reduced from FFT(1536,18) to FFT(1536,17) 24640 bit request FFT size=(1536,17) Running N+1 test using discriminant 7, base 8+sqrt(7) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1536,21) to FFT(1536,20) Reduced from FFT(1536,20) to FFT(1536,19) Reduced from FFT(1536,19) to FFT(1536,18) Reduced from FFT(1536,18) to FFT(1536,17) 24648 bit request FFT size=(1536,17) Calling N-1 BLS with factored part 0.22% and helper 0.02% (0.69% proof) (2^12451-1)/(4980401*15289230353*1143390212...2593598809) is Fermat and Lucas PRP! (5.4200s+0.0000s) [Elapsed time: 6.00 seconds]
modified2020-07-07 22:30:39
created2008-10-09 20:23:01
id100696

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