1022250 + 57913

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:

Description:1022250 + 57913
Verification status (*):PRP
Official Comment (*):ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c35 : Cami, Primo
Decimal Digits:22251   (log10 is 22250)
Rank (*):72509 (digit rank is 1)
Entrance Rank (*):57327
Currently on list? (*):no
Submitted:5/30/2014 16:24:51 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:117930
Status Flags:Verify
Score (*):34.916 (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 68
Subcategory: "ECPP"
(archival tag id 217719, tag last modified 2024-03-24 06:37:14)

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.

Pierre Cami writes (11 Sep 2014):  (report abuse)
Certificate: http://www.ellipsa.eu/public/primo/files/ecpp22251.7z

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_id117930
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"10^22250+57913" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 10^22250+57913 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 11, base 1+sqrt(11) Calling N+1 BLS with factored part 0.05% and helper 0.01% (0.17% proof) 10^22250+57913 is Fermat and Lucas PRP! (242.8553s+0.0012s) [Elapsed time: 4.05 minutes]
modified2020-07-07 22:30:17
created2014-05-30 19:22:57
id163477

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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