1591 · 2557812 + 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:1591 · 2557812 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L1524 : Bohl, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:167922   (log10 is 167921.3456115)
Rank (*):31073 (digit rank is 1)
Entrance Rank (*):4953
Currently on list? (*):no
Submitted:10/13/2010 12:17:52 CDT
Last modified:10/13/2010 13:20:34 CDT
Removed (*):10/16/2010 07:45:15 CDT
Database id:95379
Status Flags:none
Score (*):41.1503 (normalized score 0.0543)

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_id95379
person_id9
machineVista on Core 2 6700 2.66GHz
whatprime
notesCommand: pfgw.exe -n -t -q"1591*2^557812+1" 2>&1
PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Running N-1 test using base 3
N-1: 1591*2^5Primality testing 1591*2^557812+1 [N-1, Brillhart-Lehmer-Selfridge]
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
1591*2^557812+1 is prime! (1437.3878s+0.0489s)
57812+1[Elapsed time: 1437 seconds]
modified2011-12-27 16:48:37
created2010-10-13 12:43:59
id120144

fieldvalue
prime_id95379
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 1591 2 557812 1 2>&1
[Elapsed time: 9.816 seconds]
modified2011-12-27 16:48:37
created2010-10-13 12:18:01
id120138

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