E(10168)/1097239206089665

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(10168)/1097239206089665
Verification status (*):PRP
Official Comment (*):Euler irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):E10 : Doornink, CM
Decimal Digits:34323   (log10 is 34322.985064196)
Rank (*):66392 (digit rank is 1)
Entrance Rank (*):64707
Currently on list? (*):short
Submitted:10/6/2023 17:13:11 UTC
Last modified:10/6/2023 17:37:12 UTC
Database id:136513
Status Flags:Verify
Score (*):36.2556 (normalized score 0.0001)

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 2
Subcategory: "Euler Irregular primes"
(archival tag id 228858, tag last modified 2023-10-06 17:37:13)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 25
Subcategory: "ECPP"
(archival tag id 228859, tag last modified 2023-12-16 03:37:30)

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 (6 Oct 2023):  (report abuse)
Originally found to be PRP by Thomas Ritschel in 2014. 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_id136513
person_id9
machineUsing: Digital Ocean Droplet
whatprp
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -tc p_136513.txt >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 9661936881...5579284249 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 3
Generic modular reduction using generic reduction AVX-512 FFT length 12K, Pass1=192, Pass2=64, clm=1 on A 114019-bit number
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction AVX-512 FFT length 12K, Pass1=192, Pass2=64, clm=1 on A 114019-bit number
Calling N+1 BLS with factored part 0.06% and helper 0.03% (0.20% proof)


9661936881...5579284249 is Fermat and Lucas PRP! (64.4875s+0.0072s)
[Elapsed time: 65.00 seconds]
modified2023-10-06 17:15:12
created2023-10-06 17:14:01
id182347

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