(264381 - 1)/182523187856126457117740\
19109285438988204922542528174996118699181907547497
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: | (264381 - 1)/182523187856126457117740\ 19109285438988204922542528174996118699181907547497 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Mersenne cofactor, ECPP |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | E13 : Batalov, Masser, CM |
| Decimal Digits: | 19308 (log10 is 19307.350832797) |
| Rank (*): | 75158 (digit rank is 1) |
| Entrance Rank (*): | 74386 |
| Currently on list? (*): | yes |
| Submitted: | 4/11/2024 02:36:41 UTC |
| Last modified: | 4/11/2024 03:37:10 UTC |
| Database id: | 137948 |
| Status Flags: | Verify |
| Score (*): | 34.4772 (normalized score 0) |
Archival tags:
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 121
Subcategory: "ECPP"
(archival tag id 229485, tag last modified 2024-10-27 10:37:10)- Mersenne cofactor (archivable *)
- Prime on list: yes, rank 12
Subcategory: "Mersenne cofactor"
(archival tag id 229486, tag last modified 2024-09-28 08:37:11)
User comments about this prime (disclaimer):
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Verification data:
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 137948 person_id 9 machine Using: Digital Ocean Droplet what prp notes PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (2^64381-1)/1825231878...1907547497 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial
Running N-1 test using base 5
Generic modular reduction using generic reduction AVX-512 FFT length 6K on A 64138-bit number
Running N+1 test using discriminant 11, base 3+sqrt(11)
Generic modular reduction using generic reduction AVX-512 FFT length 6K on A 64138-bit number
Calling N-1 BLS with factored part 0.04% and helper 0.03% (0.15% proof)
(2^64381-1)/1825231878...1907547497 is Fermat and Lucas PRP! (35.0082s+0.0013s)
[Elapsed time: 40.00 seconds]modified 2024-04-11 02:37:42 created 2024-04-11 02:37:02 id 183790
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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