145310262144 + 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:||145310262144 + 1|
|Verification status (*):||Proven|
|Official Comment (*):||Generalized Fermat|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||p314 : Hubbard, GenefX64, AthGFNSieve, PrimeGrid, OpenPFGW|
|Decimal Digits:||1353265 (log10 is 1353264.7922789)|
|Rank (*):||482 (digit rank is 1)|
|Entrance Rank (*):||23|
|Currently on list? (*):||short|
|Submitted:||2/10/2011 05:47:24 UTC|
|Last modified:||3/11/2023 15:54:10 UTC|
|Score (*):||47.561 (normalized score 15.6774)|
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.
User comments about this prime (disclaimer):
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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 98160 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 1 145310 262144 1 2>&1 [Elapsed time: 8.635 seconds] modified 2020-07-07 22:30:32 created 2011-02-10 05:48:01 id 125680
field value prime_id 98160 person_id 9 machine Xeon 4c+4c 3.5GHz what prime notes Command: ./pfgw64 -t -q"145310^262144+1" 2>&1 PFGW Version 220.127.116.11BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 145310^262144+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 60.46% 145310^262144+1 is prime! (46438.4777s+0.0465s) [Elapsed time: 12.90 hours] modified 2020-07-07 22:30:17 created 2014-08-21 02:18:27 id 163950