731362328595 · 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:731362328595 · 21290000 - 1
Verification status (*):Proven
Official Comment:
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L3550 : Ready, TwinGen, PrimeGrid, LLR
Decimal Digits:388341   (log10 is 388340.55853912)
Rank (*):9751 (digit rank is 1080)
Entrance Rank (*):1358
Currently on list? (*):no
Submitted:7/24/2013 15:19:04 CDT
Last modified:7/24/2013 18:20:46 CDT
Removed (*):2/2/2016 08:18:45 CDT
Database id:114771
Status Flags:none
Score (*):43.7286 (normalized score 0.7152)

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.

Serge Batalov writes (12 Jun 2016): 
Arithmetic progression (1,d=496648444065*2^1290002)

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 731362328595 2 1290000 -1 2>&1
[Elapsed time: 10.366 seconds]
modified2013-08-16 09:44:42
created2013-07-24 15:35:12

machineDitto P4 P4
notesCommand: /home/ditto/client/llr.pl 731362328595*2^1290000-1 2>&1
Starting Lucas Lehmer Riesel prime test of 731362328595*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...

731362328595*2^1290000-1 is prime! Time : 5495.946 sec.
[Elapsed time: 1.53 hours]
modified2013-08-16 09:44:42
created2013-07-24 16:29:15

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