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40734262144 + 1
|Description:||40734262144 + 1|
|Verification status (*):||Proven|
|Official Comment (*):||Generalized Fermat|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||p309 : Yama, GenefX64, AthGFNSieve, PrimeGrid, OpenPFGW|
|Decimal Digits:||1208473 (log10 is 1208472.5832897)|
|Rank (*):||251 (digit rank is 1)|
|Entrance Rank (*):||26|
|Currently on list? (*):||short|
|Submitted:||3/8/2011 17:00:26 CDT|
|Last modified:||3/9/2011 04:20:21 CDT|
|Score (*):||47.2139 (normalized score 19.7711)|
There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper. Such primes are tracked with archival tags.
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.
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.
field value prime_id 99092 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 1 40734 262144 1 2>&1 [Elapsed time: 8.487 seconds] modified 2020-07-07 17:30:32 created 2011-03-08 17:05:21 id 127572
field value prime_id 99092 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"40734^262144+1" 2>&1 PFGW Version 18.104.22.168BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 40734^262144+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 40.42% 40734^262144+1 is prime! (39294.0328s+0.0909s) [Elapsed time: 10.92 hours] modified 2020-07-07 17:30:32 created 2011-03-08 17:23:01 id 127574
Query times: 0.0004 seconds to select prime, 0.0008 seconds to seek comments.
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