103939 · 2514229 - 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:103939 · 2514229 - 1
Verification status (*):Proven
Official Comment (*):Arithmetic progression (2,d=103939*2^514229-11347*2^508209)
Proof-code(s): (*):L466 : Zhou, NewPGen, LLR
Decimal Digits:154804   (log10 is 154803.37041883)
Rank (*):40409 (digit rank is 3)
Entrance Rank (*):1077
Currently on list? (*):no
Submitted:11/26/2007 16:41:07 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:83098
Status Flags:none
Score (*):40.9 (normalized score 0.0171)

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.
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 19
Subcategory: "Arithmetic progression (2,d=*)"
(archival tag id 210619, tag last modified 2023-03-11 15:53:59)

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_id83098
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 103939 2 514229 -1 2>&1 [Elapsed time: 9.603 seconds]
modified2020-07-07 22:30:40
created2007-11-26 16:52:01
id95314

fieldvalue
prime_id83098
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/llr.pl 103939*2^514229-1 2>&1 Starting Lucas Lehmer Riesel prime test of 103939*2^514229-1 V1 = 4 ; Computing U0... Done Computing U0. Starting Lucas-Lehmer loop... 103939*2^514229-1 is prime! Time : 1240.108 sec. [Elapsed time: 20.67 minutes]
modified2020-07-07 22:30:40
created2007-11-26 16:53:01
id95315

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