1681 · 21021712 + 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.
|Description:||1681 · 21021712 + 1|
|Verification status (*):||Proven|
|Official Comment (*):||Generalized Fermat|
|Proof-code(s): (*):||L2790 : Szymeczko, PSieve, Srsieve, PrimeGrid, LLR|
|Decimal Digits:||307570 (log10 is 307569.18449755)|
|Rank (*):||18374 (digit rank is 1)|
|Entrance Rank (*):||1828|
|Currently on list? (*):||no|
|Submitted:||10/9/2012 18:06:43 CDT|
|Last modified:||10/9/2012 19:20:26 CDT|
|Removed (*):||9/22/2013 21:39:29 CDT|
|Score (*):||43.0119 (normalized score 0.2054)|
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.
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 109764 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 1681 2 1021712 1 2>&1 [Elapsed time: 9.966 seconds] modified 2020-07-07 17:30:23 created 2012-10-09 18:18:23 id 149179
field value prime_id 109764 person_id 9 machine RedHat Virtual STEM Server what prime notes Command: /home/caldwell/client/pfgw -t -q"1681*2^1021712+1" 2>&1 PFGW Version 220.127.116.1100405.x86_Stable [GWNUM 25.14] Primality testing 1681*2^1021712+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 1681*2^1021712+1 is prime! (1938.0354s+0.0007s) [Elapsed time: 32.30 minutes] modified 2020-07-07 17:30:23 created 2012-10-09 18:22:44 id 149180