2 · 31074726 + 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:2 · 31074726 + 1
Verification status (*):Proven
Official Comment:
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p199 : Broadhurst, NewPGen, OpenPFGW
Decimal Digits:512775   (log10 is 512774.91862984)
Rank (*):1021 (digit rank is 1)
Entrance Rank (*):91
Currently on list? (*):yes
Submitted:2/13/2010 07:52:58 CDT
Last modified:2/17/2010 07:50:50 CDT
Database id:91746
Status Flags:none
Score (*):44.5826 (normalized score 3.0328)

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.

David Broadhurst writes (11 Sep 2014): 
See the remark in PrimeNumbers on this exception to the oligopoly of base-2 and GFN primes. On 8 August 2011, the list of the top 1000 primes contained 92 such minority representatives, of which this mega-trit prime was the 10th largest.

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_id91746
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 2 3 1074726 1 2>&1
[Elapsed time: 10.060 seconds]
modified2011-12-27 16:48:40
created2010-02-13 08:05:02
id112868

fieldvalue
prime_id91746
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"2*3^1074726+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 2*3^1074726+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(229376,19) to FFT(229376,18)
Reduced from FFT(229376,18) to FFT(229376,17)
Reduced from FFT(229376,17) to FFT(229376,16)
3406812 bit request FFT size=(229376,16)
Running N-1 test using base 3
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(229376,19) to FFT(229376,18)
Reduced from FFT(229376,18) to FFT(229376,17)
Reduced from FFT(229376,17) to FFT(229376,16)
3406812 bit request FFT size=(229376,16)
Running N-1 test using base 17
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(229376,19) to FFT(229376,18)
Reduced from FFT(229376,18) to FFT(229376,17)
Reduced from FFT(229376,17) to FFT(229376,16)
3406812 bit request FFT size=(229376,16)
Running N-1 test using base 23
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(229376,19) to FFT(229376,18)
Reduced from FFT(229376,18) to FFT(229376,17)
Reduced from FFT(229376,17) to FFT(229376,16)
3406812 bit request FFT size=(229376,16)
Running N-1 test using base 29
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(229376,19) to FFT(229376,18)
Reduced from FFT(229376,18) to FFT(229376,17)
Reduced from FFT(229376,17) to FFT(229376,16)
3406812 bit request FFT size=(229376,16)
Running N-1 test using base 31
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(229376,19) to FFT(229376,18)
Reduced from FFT(229376,18) to FFT(229376,17)
Reduced from FFT(229376,17) to FFT(229376,16)
3406812 bit request FFT size=(229376,16)
Running N-1 test using base 41
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(229376,19) to FFT(229376,18)
Reduced from FFT(229376,18) to FFT(229376,17)
Reduced from FFT(229376,17) to FFT(229376,16)
3406812 bit request FFT size=(229376,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
2*3^1074726+1 is prime! (-1665.4337s+0.1400s)
[Elapsed time: 4.00 days]
modified2010-03-13 18:56:30
created2010-02-13 07:53:01
id112867

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.