Phi(5745, - 38284)/(106238573731 · 139897540591 · 17964554195439674794086479311)
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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(5745, - 38284)/(106238573731 · 139897540591 · 17964554195439674794086479311)
Verification status (*):PRP
Official Comment:ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c54 : Wu_T, Primo
Decimal Digits:13956   (log10 is 13955.27438314)
Rank (*):68494 (digit rank is 1)
Entrance Rank (*):58295
Currently on list? (*):no
Submitted:2/10/2013 13:40:10 CDT
Last modified:2/10/2013 14:20:41 CDT
Database id:111176
Status Flags:Verify
Score (*):33.4725 (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 58
Subcategory: "ECPP"
(archival tag id 215071, tag last modified 2017-11-16 23:50:19)

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 part of the primality proof of the GRU prime Phi(11491,38284).

The Primo certificate is available from: http://www.ellipsa.eu/public/primo/files/ecpp13956.7z

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_id111176
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"Phi(5745,-38284)/(106238573731*139897540591*17964554195439674794086479311)" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Phi(5745,-38284)....674794086479311) 1/1 mro=0


trial factoring to 4118014
Phi(5745,-38284)/(106238573731*139897540591*1796455419...4086479311) has no small factor.
[Elapsed time: 5.116 seconds]
modified2013-02-16 12:06:20
created2013-02-10 13:49:21
id152627

fieldvalue
prime_id111176
person_id9
machineDitto P4 P4
whatprp
notesCommand: /home/ditto/client/pfgw -tc -q"Phi(5745,-38284)/(106238573731*139897540591*17964554195439674794086479311)" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing Phi(5745,-38284)/(106238573731*139897540591*1796455419...4086479311) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 7
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N-1 BLS with factored part 0.14% and helper 0.02% (0.42% proof)
Phi(5745,-38284)/(106238573731*139897540591*1796455419...4086479311) is Fermat and Lucas PRP! (112.3579s+0.0082s)
[Elapsed time: 1.87 minutes]
modified2013-02-16 12:06:20
created2013-02-10 14:08:01
id152629

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