10314727 - 8 · 10157363 - 1

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:10314727 - 8 · 10157363 - 1
Verification status (*):Proven
Official Comment (*):Near-repdigit, palindrome
Proof-code(s): (*):p235 : Bedwell, OpenPFGW
Decimal Digits:314727   (log10 is 314727)
Rank (*):21864 (digit rank is 1)
Entrance Rank (*):2086
Currently on list? (*):short
Submitted:1/7/2013 23:21:38 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:110658
Status Flags:none
Score (*):43.0826 (normalized score 0.1442)

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.
Near-repdigit (archivable *)
Prime on list: no, rank 47
Subcategory: "Near-repdigit"
(archival tag id 214901, tag last modified 2024-02-07 04:37:20)
Palindrome (archivable *)
Prime on list: yes, rank 15
Subcategory: "Palindrome"
(archival tag id 214902, tag last modified 2024-01-17 08:37:12)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -tp -q"10^314727-8*10^157363-1" 2>&1 PFGW Version [GWNUM 26.5] Primality testing 10^314727-8*10^157363-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Calling Brillhart-Lehmer-Selfridge with factored part 34.95% 10^314727-8*10^157363-1 is prime! (46934.4576s+0.0196s) [Elapsed time: 13.04 hours]
modified2020-07-07 22:30:23
created2013-01-07 23:23:01

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -o -f -q"10^314727-8*10^157363-1" 2>&1 PFGW Version [GWNUM 26.5] 10^314727-8*10^157363-1 1/1 mro=0 trial factoring to 115675612 10^314727-8*10^157363-1 has no small factor. [Elapsed time: 2609.883 seconds]
modified2020-07-07 22:30:23
created2013-01-07 23:35:01

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