primA(275285)
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: | primA(275285) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Lucas Aurifeuillian primitive part, ECPP |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | E1 : Batalov, CM |
| Decimal Digits: | 23012 (log10 is 23011.423625801) |
| Rank (*): | 72478 (digit rank is 1) |
| Entrance Rank (*): | 72323 |
| Currently on list? (*): | short |
| Submitted: | 3/24/2024 06:13:29 UTC |
| Last modified: | 3/24/2024 06:37:13 UTC |
| Database id: | 137870 |
| Status Flags: | Verify |
| Score (*): | 35.02 (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.
- Lucas Aurifeuillian primitive part (archivable *)
- Prime on list: yes, rank 1
Subcategory: "Lucas Aurifeuillian primitive part"
(archival tag id 229455, tag last modified 2024-03-24 06:37:15)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 69
Subcategory: "ECPP"
(archival tag id 229456, tag last modified 2024-04-24 05:37:25)
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 137870 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 2652319272...5343587651 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction AVX-512 FFT length 7680 on A 76443-bit number
Running N+1 test using discriminant 7, base 2+sqrt(7)
Generic modular reduction using generic reduction AVX-512 FFT length 7680 on A 76443-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 39/76498 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 7, base 2+sqrt(7)
Generic modular reduction using generic reduction AVX-512 FFT length 8K, Pass1=128, Pass2=64, clm=1 on A 76443-bit number
Calling N-1 BLS with factored part 0.31% and helper 0.04% (0.98% proof)
2652319272...5343587651 is Fermat and Lucas PRP! (23.3812s+0.0047s)
[Elapsed time: 25.00 seconds]modified 2024-03-24 06:14:31 created 2024-03-24 06:14:01 id 183712
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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