Phi(3, 31118781 + 1)/3
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:||Phi(3, 31118781 + 1)/3|
|Verification status (*):||Proven|
|Official Comment (*):||Generalized unique|
|Unofficial Comments:||This prime has 2 user comments below.|
|Proof-code(s): (*):||L3839 : Batalov, EMsieve, LLR|
|Decimal Digits:||1067588 (log10 is 1067587.9118318)|
|Rank (*):||668 (digit rank is 1)|
|Entrance Rank (*):||63|
|Currently on list? (*):||short|
|Submitted:||3/29/2014 04:39:12 CDT|
|Last modified:||8/22/2014 08:37:26 CDT|
|Score (*):||46.8336 (normalized score 8.3671)|
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):
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 117512 person_id 9 machine Xeon 4c+4c 3.5GHz what prime notes Command: ./pfgw64 -tc -q"Phi(3,3^1118781+1)/3" 2>&1 PFGW Version 126.96.36.199BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing Phi(3,3^1118781+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 5 Running N-1 test using base 13 Running N-1 test using base 17 Running N-1 test using base 59 Running N-1 test using base 61 Running N+1 test using discriminant 97, base 3+sqrt(97) Calling N-1 BLS with factored part 50.00% and helper 0.00% (150.01% proof) Phi(3,3^1118781+1)/3 is prime! (255252.0424s+0.3649s) [Elapsed time: 2.95 days] modified 2020-07-07 17:30:17 created 2014-08-20 21:16:36 id 163949