831542710605 · 21290000 - 1
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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:831542710605 · 21290000 - 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L3203 : Scalise, TwinGen, PrimeGrid, LLR
Decimal Digits:388341   (log10 is 388340.6142911)
Rank (*):7493 (digit rank is 985)
Entrance Rank (*):1338
Currently on list? (*):no
Submitted:8/11/2013 10:51:41 CDT
Last modified:8/11/2013 12:50:27 CDT
Removed (*):2/8/2016 12:19:35 CDT
Database id:115029
Status Flags:none
Score (*):43.7286 (normalized score 0.9928)

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_id115029
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 831542710605 2 1290000 -1 2>&1
[Elapsed time: 10.358 seconds]
modified2013-08-16 09:44:40
created2013-08-11 10:52:01
id160435

fieldvalue
prime_id115029
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/llr.pl 831542710605*2^1290000-1 2>&1
Starting Lucas Lehmer Riesel prime test of 831542710605*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...

831542710605*2^1290000-1 is prime! Time : 5621.267 sec.
[Elapsed time: 1.56 hours]
modified2013-08-16 09:44:40
created2013-08-11 10:53:01
id160437

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.