primV(11140)
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(11140) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Lucas primitive part |
| Proof-code(s): (*): | p54 : Broadhurst, Water, OpenPFGW |
| Decimal Digits: | 1860 (log10 is 1859.1631951409) |
| Rank (*): | 111361 (digit rank is 2) |
| Entrance Rank (*): | 31929 |
| Currently on list? (*): | no |
| Submitted: | 5/1/2001 16:22:14 UTC |
| Last modified: | 1/28/2026 15:10:01 UTC |
| Database id: | 37691 |
| Status Flags: | none |
| Score (*): | 27.2094 (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: no, rank 120
Subcategory: "Lucas primitive part"
(archival tag id 195693, tag last modified 2024-10-11 22:37:11)
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 37691 person_id 9 machine Using: Digital Ocean Droplet what prime notes PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 1456113206...1079110881 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000306379369
trial
Running N-1 test using base 11
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6177-bit number
Running N-1 test using base 13
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6177-bit number
Running N+1 test using discriminant 37, base 2+sqrt(37)
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6177-bit number
Calling N-1 BLS with factored part 33.05% and helper 1.83% (100.99% proof)
1456113206...1079110881 is prime! (0.3715s+0.0012s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
17
19
23
47
107
277
557
631
743
1489
2417
3347
11717
20089
30859
41143
63799
65609
103681
467729
894391
993241
2870911
3010349
4997327
9907847
15917507
35510749
253279129
618131887
775585403
1183176503
2114537501
3599504551
3020733700601
4531100550901
594960058508093
14331800109223159
33758740830460183
85526722937689093
859886421593527043
6279830532252706321
3790399876570715374441
210907424232568795946689
157945397950723345044852819601
98465083280977541404796710798431455619960794209
4807241801804168721687347232031405159192477407731041
63749871895972620649953899115136073800470980902829089
52502547128429056008972058360557876262851909903437442952759563686941760825228879521
1989470143699
4938890710010461584883modified 2026-01-28 15:10:01 created 2026-01-28 15:09:50 id 187597
field value prime_id 37691 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Reading factors from helper file helper Error opening file helper Running N-1 test using base 11 Primality testing primV(11140) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Calling Brillhart-Lehmer-Selfridge with factored part 3.59% primV(11140) is PRP! (18.920000 seconds) modified 2003-03-25 17:22:47 created 2003-01-07 05:24:42 id 63899
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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