
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:  Phi(12345, 7176)/31531760245313526865033921 
Verification status (*):  PRP 
Official Comment:  ECPP 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  c54 : Wu_T, Primo 
Decimal Digits:  25331 (log_{10} is 25330.784111701) 
Rank (*):  63218 (digit rank is 1) 
Entrance Rank (*):  61090 
Currently on list? (*):  short 
Submitted:  6/4/2017 13:54:50 CDT 
Last modified:  6/4/2017 14:20:20 CDT 
Database id:  123455 
Status Flags:  Verify, TrialDiv 
Score (*):  35.3169 (normalized score 0.0001) 

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: yes, rank 8
Subcategory: "ECPP"
(archival tag id 218758, tag last modified 20190216 16:50:05)
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  123455 
person_id  9 
machine  Using: Xeon (pool) 4c+4c 3.5GHz 
what  prp 
notes  Command: /home/caldwell/clientpool/1/pfgw64 tc q"Phi(12345,7176)/31531760245313526865033921" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing Phi(12345,7176)/3153176024...6865033921 [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 11 Running N1 test using base 13 Running N1 test using base 17 Running N+1 test using discriminant 23, base 1+sqrt(23) Calling N+1 BLS with factored part 0.05% and helper 0.05% (0.20% proof)
Phi(12345,7176)/3153176024...6865033921 is Fermat and Lucas PRP! (61.9733s+0.0043s) [Elapsed time: 62.00 seconds]

modified  20170807 13:02:22 
created  20170604 14:13:01 
id  169107 

Query times: 0.0007 seconds to select prime, 0.0008 seconds to seek comments.
