2 · 31074726 + 1

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Description:2 · 31074726 + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p199 : Broadhurst, NewPGen, OpenPFGW
Decimal Digits:512775   (log10 is 512774.91862984)
Rank (*):3210 (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 1.407)

User comments about this prime (disclaimer):

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David Broadhurst writes (11 Sep 2014):  (report abuse)
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
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]
modified2020-07-07 17:30:36
created2010-02-13 07:53:01
id112867

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]
modified2020-07-07 17:30:36
created2010-02-13 08:05:02
id112868

Query times: 0.0017 seconds to select prime, 0.0007 seconds to seek comments.
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