8409 · 21034805 + 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:||8409 · 21034805 + 1|
|Verification status (*):||Proven|
|Official Comment (*):||[none]|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||L3261 : Batalov, PSieve, Srsieve, PrimeGrid, LLR|
|Decimal Digits:||311512 (log10 is 311511.26940742)|
|Rank (*):||20113 (digit rank is 1)|
|Entrance Rank (*):||2165|
|Currently on list? (*):||no|
|Submitted:||1/14/2013 11:21:42 UTC|
|Last modified:||3/11/2023 15:54:10 UTC|
|Removed (*):||10/5/2013 11:45:13 UTC|
|Score (*):||43.0511 (normalized score 0.1759)|
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 110713 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 8409 2 1034805 1 2>&1 [Elapsed time: 10.169 seconds] modified 2020-07-07 22:30:23 created 2013-01-14 11:35:12 id 151701
field value prime_id 110713 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -t -q"8409*2^1034805+1" 2>&1 PFGW Version 18.104.22.168BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 8409*2^1034805+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 8409*2^1034805+1 is prime! (2818.0973s+0.0011s) [Elapsed time: 46.97 minutes] modified 2020-07-07 22:30:23 created 2013-01-14 12:31:11 id 151706
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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