165 · 2509812 + 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:165 · 2509812 + 1
Verification status (*):Proven
Official Comment:
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L679 : Foody, Srsieve, PrimeGrid, LLR
Decimal Digits:153471   (log10 is 153470.92163339)
Rank (*):33087 (digit rank is 1)
Entrance Rank (*):1846
Currently on list? (*):no
Submitted:1/19/2009 20:05:07 CDT
Last modified:1/20/2009 07:27:56 CDT
Removed (*):6/9/2010 00:52:54 CDT
Database id:86271
Status Flags:none
Score (*):40.8734 (normalized score 0.0426)

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.

Jim Foody writes (11 Sep 2014): 
Divides xGF(509808,10,7)

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_id86271
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 165 2 509812 1 2>&1
[Elapsed time: 11.436 seconds]
modified2011-12-27 16:48:45
created2009-01-19 20:22:02
id102010

fieldvalue
prime_id86271
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"165*2^509812+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 165*2^509812+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(65536,20) to FFT(65536,19)
Reduced from FFT(65536,19) to FFT(65536,18)
Reduced from FFT(65536,18) to FFT(65536,17)
Reduced from FFT(65536,17) to FFT(65536,16)
1019648 bit request FFT size=(65536,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
165*2^509812+1 is prime! (-2111.8573s+0.0000s)
[Elapsed time: 5.22 hours]
modified2009-02-05 12:51:35
created2009-01-19 20:56:45
id102011

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.