(23871621 - 1)/2386
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: | (23871621 - 1)/2386 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized repunit |
| Proof-code(s): (*): | p44 : Broadhurst, OpenPFGW |
| Decimal Digits: | 5473 (log10 is 5472.1211007706) |
| Rank (*): | 90645 (digit rank is 1) |
| Entrance Rank (*): | 16684 |
| Currently on list? (*): | no |
| Submitted: | 11/20/2000 23:52:26 UTC |
| Last modified: | 11/27/2024 07:53:42 UTC |
| Database id: | 23543 |
| Status Flags: | none |
| Score (*): | 30.5694 (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.
- Generalized Repunit (archivable *)
- Prime on list: no, rank 123
Subcategory: "Generalized Repunit"
(archival tag id 195013, tag last modified 2024-09-26 03:37:11)
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 23543 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper.php?id=1100000000439186861 -q"(2387^1621-1)/2386" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing (2387^1621-1)/2386 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000439186861
trial
Running N-1 test using base 23
Generic modular reduction using generic reduction AVX-512 FFT length 2K on A 18178-bit number
Running N+1 test using discriminant 43, base 12+sqrt(43)
Generic modular reduction using generic reduction AVX-512 FFT length 2K on A 18178-bit number
Calling N-1 BLS with factored part 37.18% and helper 0.13% (111.68% proof)
(2387^1621-1)/2386 is prime! (1.9049s+0.0001s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
19
31
37
41
61
109
163
181
199
271
433
541
571
613
811
1021
1069
1297
1621
1861
2161
2711
3943
4231
4357
6211
6481
9613
9721
12241
22501
30781
61561
319357
653797
2125873
2827549
5034961
5700157
8676721
11723911
54713881
765263053
1776739051
5413998043
8853421933
11043812413
24980803273
132938420437
555302951191
5230098102421
32464565879593
32478177852121
57638663314621
94308391094977
134235715729051
388848408777307
11579347569579481
18998402552786521
42388640413612201
6097606939846510507
1286740368796301962651
39388638256512755668921
566097190194177236606941
1769758980567924563141401
1846567328286799665055651
3455567943363929902967201
8511915998618156500588027
1561675537653049476317196883
3684809536240046063187950881
4151207924942226656645341441
1868063271703887783307656782671219
4092404338672245173927402328772909
95038343989504625985934328020820718649
228590772090271524874732544881389153698478769
52764948940253737720278900714116130702402427817173
37236135623422115609057484918408670965601968307598576371
1170733528373121744047827275325237593048024645805406619701824443816606516374804401
10307878983343988552994254439542491...(105 digits)...57360151019897099609839941911248713
13223305381554531487325695739546117...(122 digits)...72629695881339095756669136136111427
42974744632703823622893221523598083...(138 digits)...50450298212227214219815111077940741
12470482068701280221672078360541187...(223 digits)...05235000312029904161564108839643331
87368367754747905365809658104133730...(455 digits)...53183355041772795315533347849803361
29
285559modified 2024-11-27 07:53:42 created 2024-11-27 07:53:37 id 184808
field value prime_id 23543 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Primality testing Reading factors from helper file helper Running N-1 test using base 23 2921639399...5453820601 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 43, base 12+sqrt(43) Calling N-1 BLS with factored part 2.16% and helper 0.13% (6.62% proof) (2387^1621-1)/2386 is Fermat and Lucas PRP! (354.950000 seconds) modified 2003-03-25 17:22:46 created 2003-01-07 22:55:02 id 64198
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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