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676754262144 + 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:||676754262144 + 1|
|Verification status (*):||Proven|
|Official Comment (*):||Generalized Fermat|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||L2975 : Loureiro, GeneferCUDA, AthGFNSieve, PrimeGrid, LLR|
|Decimal Digits:||1528413 (log10 is 1528412.4598604)|
|Rank (*):||364 (digit rank is 1)|
|Entrance Rank (*):||23|
|Currently on list? (*):||short|
|Submitted:||2/13/2012 14:48:51 UTC|
|Last modified:||3/11/2023 15:54:10 UTC|
|Score (*):||47.9342 (normalized score 23.6345)|
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 95
Subcategory: "Generalized Fermat"
(archival tag id 214046, tag last modified 2023-03-25 06:37:21)
User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
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 104592 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 1 676754 262144 1 2>&1 [Elapsed time: 8.563 seconds] modified 2020-07-07 22:30:28 created 2012-02-13 14:52:02 id 138774
field value prime_id 104592 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"676754^262144+1" 2>&1 PFGW Version 184.108.40.206BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 676754^262144+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 75.73% 676754^262144+1 is prime! (383467.2930s+0.1193s) [Elapsed time: 4.44 days] modified 2020-07-07 22:30:28 created 2012-02-13 14:53:01 id 138775
Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
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