
At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:
field (help)  value 
Description:  V(45953)/4561241750239 
Verification status (*):  PRP 
Official Comment:  Lucas cofactor, ECPP 
Unofficial Comments:  This prime has 2 user comments below. 
Proofcode(s): (*):  c56 : Soule, Minovic, OpenPFGW, Primo 
Decimal Digits:  9591 (log_{10} is 9590.9499493164) 
Rank (*):  74266 (digit rank is 1) 
Entrance Rank (*):  58526 
Currently on list? (*):  short 
Submitted:  3/29/2012 05:37:04 CDT 
Last modified:  3/29/2012 08:02:54 CDT 
Database id:  105913 
Status Flags:  Verify 
Score (*):  32.3106 (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 185
Subcategory: "ECPP"
(archival tag id 214251, tag last modified 20180722 00:50:24)  Lucas cofactor (archivable *)
 Prime on list: yes, rank 8
Subcategory: "Lucas cofactor"
(archival tag id 214252, tag last modified 20150312 17:20:33)
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.
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.
field  value 
prime_id  105913 
person_id  9 
machine  Ditto P4 P4 
what  prp 
notes  Command: /home/ditto/client/pfgw tc q"V(45953)/4561241750239" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing V(45953)/4561241750239 [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 2 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N+1 BLS with factored part 0.13% and helper 0.08% (0.48% proof) V(45953)/4561241750239 is Fermat and Lucas PRP! (32.4335s+0.0038s) [Elapsed time: 33.00 seconds]

modified  20120716 11:33:01 
created  20120329 05:38:01 
id  141409 

field  value 
prime_id  105913 
person_id  9 
machine  RedHat P4 P4 
what  trial_divided 
notes  Command: /home/caldwell/client/pfgw o f q"V(45953)/4561241750239" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] V(45953)/4561241750239 1/1 mro=0
trial factoring to 2746508 V(45953)/4561241750239 has no small factor. [Elapsed time: 2.559 seconds]

modified  20120716 11:33:01 
created  20120329 05:48:51 
id  141417 

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.
