Phi(4641, 32556)/(258503701 · 84419168107)
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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(4641, 32556)/(258503701 · 84419168107)
Verification status (*):PRP
Official Comment:ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c54 : Wu_T, Primo
Decimal Digits:10378   (log10 is 10377.763007887)
Rank (*):73330 (digit rank is 1)
Entrance Rank (*):52443
Currently on list? (*):no
Submitted:4/22/2011 02:56:46 CDT
Last modified:4/22/2011 03:20:29 CDT
Database id:99794
Status Flags:Verify
Score (*):32.555 (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 155
Subcategory: "ECPP"
(archival tag id 213218, tag last modified 2018-06-17 18:50:23)

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.

Tom Wu writes (11 Sep 2014): 
This number is a helper for the CHG proof of the GRU prime N=Phi(9283,32556), providing 24.776% of the factorization of N-1. The Primo certificate was generated in about 3 months using multiple processors and is available at:
The expression for this prime can also be written as Phi(4641,32556)/(9283*27847*84419168107).

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -o -f -q"Phi(4641,32556)/(258503701*84419168107)" 2>&1
PFGW Version [GWNUM 26.5]
Phi(4641,32556)/....701*84419168107) 1/1 mro=0

trial factoring to 2990877
Phi(4641,32556)/(258503701*84419168107) has no small factor.
[Elapsed time: 2.857 seconds]
modified2011-12-27 16:48:33
created2011-04-22 03:05:01

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -tc -q"Phi(4641,32556)/(258503701*84419168107)" 2>&1
PFGW Version [GWNUM 26.5]
Primality testing Phi(4641,32556)/(258503701*84419168107) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 1+sqrt(5)
Calling N+1 BLS with factored part 0.09% and helper 0.06% (0.34% proof)
Phi(4641,32556)/(258503701*84419168107) is Fermat and Lucas PRP! (45.8252s+0.0046s)
[Elapsed time: 45.00 seconds]
modified2011-05-17 08:18:58
created2011-04-22 03:08:02

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