354721848567 · 21290000 - 1
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help)value
Description:354721848567 · 21290000 - 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L2379 : Doom, TwinGen, PrimeGrid, LLR
Decimal Digits:388341   (log10 is 388340.24429447)
Rank (*):10084 (digit rank is 1417)
Entrance Rank (*):1090
Currently on list? (*):no
Submitted:2/21/2013 21:15:01 CDT
Last modified:2/21/2013 23:20:26 CDT
Removed (*):11/17/2015 13:19:12 CDT
Database id:111306
Status Flags:none
Score (*):43.7286 (normalized score 0.7157)

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_id111306
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 354721848567 2 1290000 -1 2>&1
[Elapsed time: 10.223 seconds]
modified2013-02-24 16:44:13
created2013-02-21 21:18:43
id152888

fieldvalue
prime_id111306
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/llr.pl 354721848567*2^1290000-1 2>&1
Starting Lucas Lehmer Riesel prime test of 354721848567*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...

354721848567*2^1290000-1 is prime! Time : 5556.593 sec.
[Elapsed time: 1.54 hours]
modified2013-02-24 16:44:13
created2013-02-21 21:38:02
id152891

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