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69318339141 · 2371# + 1
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:||69318339141 · 2371# + 1|
|Verification status (*):||Proven|
|Official Comment (*):||Arithmetic progression (9,d=1298717501*2371#)|
|Proof-code(s): (*):||p308 : DavisK, Underwood, NewPGen, PrimeForm_egroup, OpenPFGW|
|Decimal Digits:||1014 (log10 is 1013.5910308424)|
|Rank (*):||127197 (digit rank is 1923)|
|Entrance Rank (*):||93457|
|Currently on list? (*):||short|
|Submitted:||8/1/2011 01:09:49 UTC|
|Last modified:||3/11/2023 15:54:10 UTC|
|Score (*):||25.3142 (normalized score 0)|
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.
- Arithmetic Progressions of Primes (archivable class *)
- Prime on list: yes, rank 5, weight 51.343569876828
Subcategory: "Arithmetic progression (9,d=*)"
(archival tag id 213339, tag last modified 2023-03-11 15:53:59)
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 100962 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 69318339141 2371 # 1 2>&1 [Elapsed time: 143.032 seconds] modified 2020-07-07 22:30:31 created 2011-08-01 01:18:01 id 131474
field value prime_id 100962 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"69318339141*2371#+1" 2>&1 PFGW Version 184.108.40.206BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 69318339141*2371#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 33.59% 69318339141*2371#+1 is prime! (0.3241s+0.0003s) [Elapsed time: 0.00 seconds] modified 2020-07-07 22:30:31 created 2011-08-01 01:23:02 id 131493
Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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