(14665 · 1034110 - 56641)/9999

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:(14665 · 1034110 - 56641)/9999
Verification status (*):PRP
Official Comment (*):ECPP, Palindrome
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):c89 : Broadhurst, Underwood, Primo
Decimal Digits:34111   (log10 is 34110.166325499)
Rank (*):66513 (digit rank is 1)
Entrance Rank (*):57092
Currently on list? (*):no
Submitted:3/29/2018 22:38:40 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:124558
Status Flags:Verify
Score (*):36.2364 (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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 26
Subcategory: "ECPP"
(archival tag id 219093, tag last modified 2023-12-16 03:37:30)
Palindrome (archivable *)
Prime on list: no, rank 170
Subcategory: "Palindrome"
(archival tag id 219094, tag last modified 2024-01-17 08:37:12)

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.

David Broadhurst writes (31 Mar 2018):  (report abuse)
The decimal expansion of this palindromic prime contains 8527 instances of Nelson Mandela's prison number, 46664. This number of instances is less than the number of days that elapsed between his sentence of life imprisonment, on 12 June 1964, and his release from jail, on 11 February 1990. In October 2003, he said "46664 was my prison number. For over 18 years I was imprisoned on Robben Island, known just as a number. Millions of people today infected with AIDS are just that - a number. They too are serving a prison sentence - for life."

Paul Underwood writes (1 Apr 2018):  (report abuse)
The certificate is here. David Broadhurst's PRP is here.

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: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tc -q"(14665*10^34110-56641)/9999" 2>&1 PFGW Version [GWNUM 27.11] Primality testing (14665*10^34110-56641)/9999 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Running N+1 test using discriminant 19, base 15+sqrt(19) Calling N-1 BLS with factored part 0.03% and helper 0.03% (0.14% proof) (14665*10^34110-56641)/9999 is Fermat and Lucas PRP! (94.7432s+0.0007s) [Elapsed time: 1.58 minutes]
modified2020-07-07 22:30:15
created2018-03-29 22:41:01

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