31 · 28348000 + 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:||31 · 28348000 + 1|
|Verification status (*):||Proven|
|Official Comment (*):||[none]|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||L5229 : Karpenko, LLR2, PSieve, Srsieve, PrimeGrid, LLR|
|Decimal Digits:||2513000 (log10 is 2512999.8951646)|
|Rank (*):||152 (digit rank is 1)|
|Entrance Rank (*):||73|
|Currently on list? (*):||short|
|Submitted:||1/20/2021 01:08:43 UTC|
|Last modified:||5/20/2023 20:59:19 UTC|
|Score (*):||49.4584 (normalized score 103.3689)|
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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 131593 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prime notes Command: /home/caldwell/clientpool/1/pfgw64 -t -q"31*2^8348000+1" 2>&1 PFGW Version 188.8.131.52BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 31*2^8348000+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 31*2^8348000+1 is prime! (26044.2793s+0.0039s) [Elapsed time: 7.23 hours] modified 2021-04-20 22:39:25 created 2021-01-20 01:11:01 id 177289