1040000 + 14253

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:1040000 + 14253
Verification status (*):PRP
Official Comment (*):ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):E3 : Enge, CM
Decimal Digits:40001   (log10 is 40000)
Rank (*):61360 (digit rank is 2)
Entrance Rank (*):60892
Currently on list? (*):short
Submitted:6/22/2022 09:13:42 CDT
Last modified:6/22/2022 09:37:19 CDT
Database id:134073
Status Flags:Verify, TrialDiv
Score (*):36.7283 (normalized score 0.0003)

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: yes, rank 5
Subcategory: "ECPP"
(archival tag id 227139, tag last modified 2022-09-09 14:37:23)

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.

Andreas Enge writes (22 Jun 2022):  (report abuse)
Certificate available on the CM website, checked by factordb.

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.
machineUsing: Dual Intel Xeon Gold 5222 CPUs 3.8GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"10^40000+14253" 2>&1 PFGW Version [GWNUM 29.8] Primality testing 10^40000+14253 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 5 Running N-1 test using base 7 Running N-1 test using base 13 Running N-1 test using base 23 Running N+1 test using discriminant 31, base 3+sqrt(31) Calling N+1 BLS with factored part 0.02% and helper 0.02% (0.08% proof) 10^40000+14253 is Fermat and Lucas PRP! (33.0164s+0.0002s) [Elapsed time: 33.00 seconds]
modified2022-07-11 13:21:44
created2022-06-22 09:16:01

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