4404139952163 · 267002 - 5
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: | 4404139952163 · 267002 - 5 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Triplet (1), ECPP |
| Proof-code(s): (*): | E15 : Batalov, PolySieve, CM |
| Decimal Digits: | 20183 (log10 is 20182.255630589) |
| Rank (*): | 73982 (digit rank is 3) |
| Entrance Rank (*): | 73489 |
| Currently on list? (*): | yes |
| Submitted: | 7/11/2024 00:23:39 UTC |
| Last modified: | 7/11/2024 00:37:11 UTC |
| Database id: | 138293 |
| Status Flags: | Verify |
| Score (*): | 34.6143 (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 114
Subcategory: "ECPP"
(archival tag id 229592, tag last modified 2024-12-16 19:37:11)- Triplet (archivable class *)
- Prime on list: yes, rank 1
Subcategory: "Triplet (1)"
(archival tag id 229593, tag last modified 2024-07-11 00:37:13)
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 138293 person_id 9 machine Using: Digital Ocean Droplet what prp notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"4404139952163*2^67002-5" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 4404139952163*2^67002-5 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial
Running N-1 test using base 2
Special modular reduction using zero-padded AVX-512 FFT length 7K on 4404139952163*2^67002-5
Running N+1 test using discriminant 5, base 1+sqrt(5)
Special modular reduction using zero-padded AVX-512 FFT length 7K on 4404139952163*2^67002-5
Calling N+1 BLS with factored part 0.01% and helper 0.01% (0.06% proof)
4404139952163*2^67002-5 is Fermat and Lucas PRP! (6.9838s+0.0087s)
[Elapsed time: 10.00 seconds]modified 2024-07-11 00:24:12 created 2024-07-11 00:24:02 id 184135
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.