U(32077)/153087505413829037510511957221947361
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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:U(32077)/153087505413829037510511957221947361
Verification status (*):PRP
Official Comment:Fibonacci cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c8 : Water, Broadhurst, Primo
Decimal Digits:6669   (log10 is 6668.1621115502)
Rank (*):77470 (digit rank is 2)
Entrance Rank (*):68130
Currently on list? (*):short
Submitted:5/23/2013 16:02:50 CDT
Last modified:5/23/2013 16:20:34 CDT
Database id:114230
Status Flags:Verify
Score (*):31.1832 (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 285
Subcategory: "ECPP"
(archival tag id 217170, tag last modified 2017-10-14 12:20:21)
Fibonacci cofactor (archivable *)
Prime on list: yes, rank 17
Subcategory: "Fibonacci cofactor"
(archival tag id 217171, tag last modified 2017-04-14 17:50:17)

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): 
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_id114230
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/pfgw -o -f -q"U(32077)/153087505413829037510511957221947361" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
U(32077)/1530875....0511957221947361 1/1 mro=0


trial factoring to 1853184
U(32077)/1530875054...7221947361 has no small factor.
[Elapsed time: 1.177 seconds]
modified2013-06-04 07:30:39
created2013-05-23 16:05:04
id158834

fieldvalue
prime_id114230
person_id9
machineDitto P4 P4
whatprp
notesCommand: /home/ditto/client/pfgw -tc -q"U(32077)/153087505413829037510511957221947361" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing U(32077)/1530875054...7221947361 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 6+sqrt(13)
Calling N+1 BLS with factored part 0.14% and helper 0.02% (0.43% proof)
U(32077)/1530875054...7221947361 is Fermat and Lucas PRP! (17.0842s+0.0009s)
[Elapsed time: 17.00 seconds]
modified2013-06-04 07:30:39
created2013-05-23 16:08:38
id158838

Query times: 0.0004 seconds to select prime, 0.001 seconds to seek comments.