723 · 21318416 + 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:723 · 21318416 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L1204 : Brown1, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:396886   (log10 is 396885.62190162)
Rank (*):6617 (digit rank is 1)
Entrance Rank (*):429
Currently on list? (*):no
Submitted:1/20/2012 11:20:01 CDT
Last modified:1/20/2012 12:20:24 CDT
Removed (*):2/11/2018 18:00:22 CDT
Database id:103972
Status Flags:none
Score (*):43.7955 (normalized score 0.783)

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.
machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -t -q"723*2^1318416+1" 2>&1
PFGW Version [GWNUM 25.14]
Primality testing 723*2^1318416+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
723*2^1318416+1 is prime! (2264.1102s+0.0300s)
[Elapsed time: 37.90 minutes]
modified2012-02-19 19:07:48
created2012-01-20 11:30:23

machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 723 2 1318416 1 2>&1
[Elapsed time: 9.747 seconds]
modified2012-02-19 19:07:48
created2012-01-20 11:35:01

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