689186131072 + 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:||689186131072 + 1|
|Verification status (*):||Proven|
|Official Comment (*):||Generalized Fermat|
|Proof-code(s): (*):||g429 : Underbakke, GenefX64, AthGFNSieve, PrimeGrid, Proth.exe|
|Decimal Digits:||765243 (log10 is 765242.43474001)|
|Rank (*):||3100 (digit rank is 1)|
|Entrance Rank (*):||105|
|Currently on list? (*):||yes|
|Submitted:||2/5/2013 23:31:26 UTC|
|Last modified:||3/11/2023 15:54:10 UTC|
|Score (*):||45.8119 (normalized score 2.7877)|
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.
- Generalized Fermat (archivable *)
- Prime on list: no, rank 966
Subcategory: "Generalized Fermat"
(archival tag id 215068, tag last modified 2023-05-29 18:37:15)
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 111122 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 1 689186 131072 1 2>&1 [Elapsed time: 8.243 seconds] modified 2020-07-07 22:30:23 created 2013-02-05 23:35:02 id 152518
field value prime_id 111122 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -t -q"689186^131072+1" 2>&1 PFGW Version 220.127.116.11BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 689186^131072+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 48.48% 689186^131072+1 is prime! (95156.2438s+0.0531s) [Elapsed time: 26.43 hours] modified 2020-07-07 22:30:23 created 2013-02-05 23:38:01 id 152519
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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