3214654524288 + 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:||3214654524288 + 1|
|Verification status (*):||Proven|
|Official Comment (*):||Generalized Fermat|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||L4309 : Kecic, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR|
|Decimal Digits:||3411613 (log10 is 3411612.3941893)|
|Rank (*):||79 (digit rank is 1)|
|Entrance Rank (*):||30|
|Currently on list? (*):||short|
|Submitted:||12/25/2019 06:02:28 CDT|
|Last modified:||12/29/2019 11:50:20 CDT|
|Score (*):||50.395 (normalized score 311.4522)|
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 130199 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prime notes Command: /home/caldwell/client/pfgw/pfgw64 -t -q"3214654^524288+1" 2>&1 PFGW Version 188.8.131.52BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 3214654^524288+1 [N-1, Brillhart-Lehmer-Selfridge] F: 3214654^524288+1 16384/36012170 (trial factor to 1442980243) F: 3214654^524288+1 34816/36012170 (trial factor to 1442980243) F: 3214654^524288+1 53248/36012170 (trial factor to 1442980243) Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 95.37% 3214654^524288+1 is prime! (364920.2327s+0.1426s) [Elapsed time: 4.22 days] modified 2020-07-07 17:30:10 created 2019-12-25 06:11:02 id 175885