685 · 21378573 - 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.
|Description:||685 · 21378573 - 1|
|Verification status (*):||Proven|
|Official Comment (*):||[none]|
|Proof-code(s): (*):||L1809 : Vogel, PSieve, Srsieve, NPLB, LLR|
|Decimal Digits:||414995 (log10 is 414994.65990305)|
|Rank (*):||8782 (digit rank is 1)|
|Entrance Rank (*):||1812|
|Currently on list? (*):||no|
|Submitted:||11/25/2014 01:57:59 CDT|
|Last modified:||11/25/2014 02:37:39 CDT|
|Removed (*):||2/4/2019 11:19:32 CDT|
|Score (*):||43.9326 (normalized score 0.5758)|
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 118816 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prime notes Command: /home/caldwell/clientpool/1/pfgw64 -tp -q"685*2^1378573-1" 2>&1 PFGW Version 18.104.22.168BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 685*2^1378573-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 685*2^1378573-1 is prime! (2197.3816s+0.0007s) [Elapsed time: 36.62 minutes] modified 2020-07-07 17:30:17 created 2014-11-25 02:01:02 id 164404