(3412011311 - 1)/34119
At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: 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:
|Description:||(3412011311 - 1)/34119|
|Verification status (*):||PRP|
|Official Comment (*):||Generalized repunit|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||CH2 : Wu_T, OpenPFGW, Primo, CHG|
|Decimal Digits:||51269 (log10 is 51268.332057152)|
|Rank (*):||57169 (digit rank is 2)|
|Entrance Rank (*):||32834|
|Currently on list? (*):||short|
|Submitted:||9/1/2011 14:53:48 CDT|
|Last modified:||9/1/2011 15:50:25 CDT|
|Score (*):||37.4943 (normalized score 0.0008)|
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.
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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 101439 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f -q"(34120^11311-1)/34119" 2>&1 PFGW Version 18.104.22.168BIT.20110215.x86_Dev [GWNUM 26.5] (34120^11311-1)/34119 1/1 mro=0 trial factoring to 16679901 (34120^11311-1)/34119 has no small factor. [Elapsed time: 68.275 seconds] modified 2020-07-07 17:30:31 created 2011-09-01 15:05:05 id 132443
field value prime_id 101439 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -tc -q"(34120^11311-1)/34119" 2>&1 PFGW Version 22.214.171.124BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing (34120^11311-1)/34119 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Running N+1 test using discriminant 37, base 15+sqrt(37) Calling N-1 BLS with factored part 0.36% and helper 0.01% (1.08% proof) (34120^11311-1)/34119 is Fermat and Lucas PRP! (1436.7923s+0.0283s) [Elapsed time: 23.95 minutes] modified 2020-07-07 17:30:31 created 2011-09-01 15:23:01 id 132445