At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: 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:

Verification status (*):PRP
Official Comment (*):Fibonacci cofactor, ECPP
Proof-code(s): (*):c8 : Broadhurst, Water, Primo
Decimal Digits:7213   (log10 is 7212.968891043)
Rank (*):84980 (digit rank is 1)
Entrance Rank (*):67325
Currently on list? (*):short
Submitted:7/1/2013 14:01:19 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:114542
Status Flags:Verify
Score (*):31.4269 (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 423
Subcategory: "ECPP"
(archival tag id 217196, tag last modified 2023-11-19 15:37:04)
Fibonacci cofactor (archivable *)
Prime on list: yes, rank 20
Subcategory: "Fibonacci cofactor"
(archival tag id 217197, tag last modified 2023-03-11 15:53:59)

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"U(34607)/13088506284255296513" 2>&1 PFGW Version [GWNUM 26.5] U(34607)/13088506284255296513 1/1 mro=0 trial factoring to 2017693 U(34607)/13088506284255296513 has no small factor. [Elapsed time: 1.800 seconds]
modified2020-07-07 22:30:19
created2013-07-01 14:05:02

machineWinXP Dual Core 2.6GHz 32-bit
notesCommand: pfgw32.exe -tc -q"U(34607)/13088506284255296513" 2>&1 PFGW Version [GWNUM 27.8] Primality testing U(34607)/13088506284255296513 [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 13, base 1+sqrt(13) Calling N-1 BLS with factored part 0.28% and helper 0.20% (1.04% proof) U(34607)/13088506284255296513 is Fermat and Lucas PRP! (15.5675s+0.0028s) [Elapsed time: 17 seconds]
modified2020-07-07 22:30:19
created2013-07-01 14:30:06

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.