29122578021 · 2333333 - 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:29122578021 · 2333333 - 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L255 : Kramer, NewPGen, PrimeGrid, TPS, LLR
Decimal Digits:100354   (log10 is 100353.69577448)
Rank (*):41291 (digit rank is 698)
Entrance Rank (*):4433
Currently on list? (*):no
Submitted:1/14/2008 09:48:26 CDT
Last modified:1/16/2008 09:27:08 CDT
Removed (*):2/20/2008 07:10:05 CDT
Database id:83557
Status Flags:none
Score (*):39.5651 (normalized score 0.0119)

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_id83557
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 29122578021 2 333333 -1 2>&1
[Elapsed time: 9.640 seconds]
modified2011-12-27 16:48:48
created2008-01-14 09:54:56
id96215

fieldvalue
prime_id83557
person_id9
machineWinXP Pent_M 1.7GHz Laptop
whatprime
notesCommand: pfgw.exe -n -tp -q"29122578021*2^333333-1" 2>&1
Primality testing 29122578021*2^333333-1 [N+1, Brillhart-Lehmer-Selfridge]
PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Running N+1 test using discriminant 7, base 1+sqrt(7)
N+1: 29122578021*2^333333-1 2Calling Brillhart-Lehmer-Selfridge with factored part 99.99%
29122578021*2^333333-1 is prime! (11606.2283s+0.0332s)
25000/333369
[Elapsed time: 11608 seconds]
modified2011-12-27 16:48:48
created2008-01-16 06:13:39
id96429

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