349574475297 · 21290000 - 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.

Description:349574475297 · 21290000 - 1
Verification status (*):Proven
Official Comment (*):Arithmetic progression (1,d=477145708425*2^1290001) [p199]
Proof-code(s): (*):L2379 : Doom, TwinGen, PrimeGrid, LLR
Decimal Digits:388341   (log10 is 388340.23794625)
Rank (*):11347 (digit rank is 1422)
Entrance Rank (*):1178
Currently on list? (*):no
Submitted:3/7/2013 10:33:59 CDT
Last modified:10/17/2015 19:18:19 CDT
Database id:111514
Status Flags:none
Score (*):43.7286 (normalized score 0.5926)

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.

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_id111514
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 349574475297 2 1290000 -1 2>&1 [Elapsed time: 10.341 seconds]
modified2020-07-07 17:30:22
created2013-03-07 10:35:12
id153345

fieldvalue
prime_id111514
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/llr.pl 349574475297*2^1290000-1 2>&1 Starting Lucas Lehmer Riesel prime test of 349574475297*2^1290000-1 Using Zero Padded IBDWT : Mersenne fftlen = 65536, Used fftlen = 131072 V1 = 5 ; Computing U0... V1 = 5 ; Computing U0...done. Starting Lucas-Lehmer loop... 349574475297*2^1290000-1 is prime! Time : 5657.932 sec. [Elapsed time: 1.57 hours]
modified2020-07-07 17:30:22
created2013-03-07 12:44:19
id153352

Query times: 0.0001 seconds to select prime, 0.0002 seconds to seek comments.
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