(251487 - 1)/57410994232247 / 17292148963401772464767849635553
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:||(251487 - 1)/57410994232247 / 17292148963401772464767849635553|
|Verification status (*):||PRP|
|Official Comment (*):||Mersenne cofactor, ECPP|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||c77 : Batalov, Primo|
|Decimal Digits:||15455 (log10 is 15454.134542715)|
|Rank (*):||72774 (digit rank is 2)|
|Entrance Rank (*):||67820|
|Currently on list? (*):||short|
|Submitted:||11/4/2018 20:20:19 CDT|
|Last modified:||11/4/2018 20:50:17 CDT|
|Status Flags:||Verify, TrialDiv|
|Score (*):||33.7884 (normalized score 0)|
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.
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 107
(archival tag id 219948, tag last modified 2022-06-26 16:37:20)
- Mersenne cofactor (archivable *)
- Prime on list: yes, rank 11
Subcategory: "Mersenne cofactor"
(archival tag id 219949, tag last modified 2022-06-13 13:37:10)
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 125757 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"(2^51487-1)/57410994232247/17292148963401772464767849635553" 2>&1 PFGW Version 188.8.131.52BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing (2^51487-1)/57410994232247/1729214896...7849635553 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 13, base 12+sqrt(13) Calling N-1 BLS with factored part 0.11% and helper 0.08% (0.40% proof) (2^51487-1)/57410994232247/1729214896...7849635553 is Fermat and Lucas PRP! (16.1966s+0.0003s) [Elapsed time: 17.00 seconds] modified 2020-07-07 17:30:14 created 2018-11-04 20:21:01 id 171434