primV(194181)
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: | primV(194181) |
|---|---|
| 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: | 24908 (log10 is 24907.982917153) |
| Rank (*): | 72117 (digit rank is 1) |
| Entrance Rank (*): | 72006 |
| Currently on list? (*): | yes |
| Submitted: | 10/11/2024 20:39:22 UTC |
| Last modified: | 10/11/2024 22:37:09 UTC |
| Database id: | 138639 |
| Status Flags: | Verify |
| Score (*): | 35.2649 (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 primitive part (archivable *)
- Prime on list: yes, rank 2
Subcategory: "Lucas primitive part"
(archival tag id 229694, tag last modified 2024-10-11 22:37:11)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 63
Subcategory: "ECPP"
(archival tag id 229695, tag last modified 2024-10-27 10:37:10)
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.
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 138639 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 9614288574...2347371521 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial
Running N-1 test using base 17
Generic modular reduction using generic reduction AVX-512 FFT length 8K, Pass1=128, Pass2=64, clm=1 on A 82743-bit number
Running N-1 test using base 19
Generic modular reduction using generic reduction AVX-512 FFT length 8K, Pass1=128, Pass2=64, clm=1 on A 82743-bit number
Running N-1 test using base 31
Generic modular reduction using generic reduction AVX-512 FFT length 8K, Pass1=128, Pass2=64, clm=1 on A 82743-bit number
Running N+1 test using discriminant 59, base 5+sqrt(59)
Generic modular reduction using generic reduction AVX-512 FFT length 8K, Pass1=128, Pass2=64, clm=1 on A 82743-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 10297/82777 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 59, base 5+sqrt(59)
Generic modular reduction using generic reduction AVX-512 FFT length 9K on A 82743-bit number
Calling N-1 BLS with factored part 0.55% and helper 0.03% (1.69% proof)
9614288574...2347371521 is Fermat and Lucas PRP! (39.0935s+0.0045s)
[Elapsed time: 40.00 seconds]modified 2024-10-11 21:46:26 created 2024-10-11 21:45:41 id 184483
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.