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:
|Verification status (*):||PRP|
|Official Comment (*):||Partitions, ECPP|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||E1 : Batalov, CM|
|Decimal Digits:||20000 (log10 is 19999.749690972)|
|Rank (*):||69806 (digit rank is 2)|
|Entrance Rank (*):||69492|
|Currently on list? (*):||short|
|Submitted:||6/27/2022 19:53:40 CDT|
|Last modified:||7/11/2022 11:50:09 CDT|
|Blob database id:||412|
|Status Flags:||Verify, TrialDiv|
|Score (*):||34.5862 (normalized score 0)|
Description: (from blob table id=412)
The number of unrestricted integer partitions of 322610098 is p(322610098).
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 134096 person_id 9 machine Using: Dual Intel Xeon Gold 5222 CPUs 3.8GHz what prp notes PFGW Version 220.127.116.11BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 5619413257...2440863153 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 11, base 1+sqrt(11) Calling N+1 BLS with factored part 0.08% and helper 0.01% (0.24% proof) 5619413257...2440863153 is Fermat and Lucas PRP! (10.2557s+0.0015s) [Elapsed time: 10.00 seconds] modified 2022-07-11 13:21:44 created 2022-07-11 11:48:00 id 179889