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.
|Verification status (*):||PRP|
|Official Comment (*):||Lucas primitive part, ECPP|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||E1 : Batalov, CM|
|Decimal Digits:||17696 (log10 is 17695.585044474)|
|Rank (*):||71753 (digit rank is 1)|
|Entrance Rank (*):||71620|
|Currently on list? (*):||short|
|Submitted:||5/17/2022 17:59:20 CDT|
|Last modified:||5/23/2022 22:40:15 CDT|
|Status Flags:||Verify, TrialDiv|
|Score (*):||34.2075 (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.
- Lucas primitive part (archivable *)
- Prime on list: yes, rank 6
Subcategory: "Lucas primitive part"
(archival tag id 227051, tag last modified 2022-06-05 13:37:19)
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 77
(archival tag id 227052, tag last modified 2022-07-03 06:37:26)
User comments about this prime (disclaimer):
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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 133944 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 3846311681...0200562881 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 31
Running N+1 test using discriminant 43, base 19+sqrt(43)
Calling N-1 BLS with factored part 0.63% and helper 0.04% (1.95% proof)
3846311681...0200562881 is Fermat and Lucas PRP! (7.7494s+0.0013s)
[Elapsed time: 7.00 seconds]
modified 2022-05-17 18:01:09 created 2022-05-17 18:01:02 id 179668
field value prime_id 133944 person_id 9 machine Using: Dual Intel Xeon Gold 5222 CPUs 3.8GHz what requested notes pfgw modified 2022-05-17 18:01:01 created 2022-05-17 18:01:01 id 179667