- E(7634)/1559

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: - E(7634)/1559
Verification status (*):External
Official Comment (*):Euler irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):E10 : Doornink, CM
Decimal Digits:24828   (log10 is 24827.599274609)
Rank (*):71701 (digit rank is 1)
Entrance Rank (*):69504
Currently on list? (*):short
Submitted:5/12/2023 10:12:09 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:136039
Status Flags:none
Score (*):35.2549 (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.
Euler Irregular primes (archivable *)
Prime on list: yes, rank 5
Subcategory: "Euler Irregular primes"
(archival tag id 228554, tag last modified 2023-10-06 17:37:13)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 59
Subcategory: "ECPP"
(archival tag id 228555, tag last modified 2024-04-24 05:37:25)

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.

Frank Doornink writes (12 May 2023):  (report abuse)
Originally found to be PRP by David Broadhurst in 2006. For certificate see 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.
fieldvalue
prime_id136039
person_id9
machineUsing: Digital Ocean Droplet
whatprp
notesPFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 3974427771...3970616759 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Generic modular reduction using generic reduction AVX-512 FFT length 8K, Pass1=128, Pass2=64, clm=1 on A 82476-bit number
Running N+1 test using discriminant 17, base 1+sqrt(17)
Generic modular reduction using generic reduction AVX-512 FFT length 8K, Pass1=128, Pass2=64, clm=1 on A 82476-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 57005/82497 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 17, base 1+sqrt(17)
Generic modular reduction using generic reduction AVX-512 FFT length 9K on A 82476-bit number
Calling N-1 BLS with factored part 0.02% and helper 0.01% (0.07% proof)


3974427771...3970616759 is Fermat and Lucas PRP! (46.0199s+0.0067s)
[Elapsed time: 47.00 seconds]
modified2023-05-12 15:25:34
created2023-05-12 15:24:47
id181862

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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