primV(10514)
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(10514) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Lucas primitive part, APR-CL assisted |
| Proof-code(s): (*): | F3 : Broadhurst, Water, VFYPR |
| Decimal Digits: | 1881 (log10 is 1880.9479076129) |
| Rank (*): | 111360 (digit rank is 1) |
| Entrance Rank (*): | 32120 |
| Currently on list? (*): | no |
| Submitted: | 5/21/2001 12:00:54 UTC |
| Last modified: | 1/28/2026 14:51:27 UTC |
| Database id: | 37624 |
| Status Flags: | none |
| Score (*): | 27.2457 (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.
- APR-CL assisted (tolerated *)
- Prime on list: no, rank 44
Subcategory: "APR-CL assisted"
(archival tag id 176271, tag last modified 2023-03-11 15:53:59)- Lucas primitive part (archivable *)
- Prime on list: no, rank 119
Subcategory: "Lucas primitive part"
(archival tag id 195692, 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 37624 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 8869673081...0912970001 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000306327893
trial
Running N-1 test using base 13
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6249-bit number
Running N+1 test using discriminant 29, base 4+sqrt(29)
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 6249-bit number
Calling N-1 BLS with factored part 33.58% and helper 0.90% (101.63% proof)
8869673081...0912970001 is prime! (0.3242s+0.0015s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
31
41
47
61
101
151
251
401
563
601
751
2207
2251
2521
3001
5641
6869
9001
12301
18049
18451
100769
169501
570601
10779169
112128001
230686501
1353439001
2971215073
3547078721
6643838879
28143378001
59017617247
329233146001
1844139855023
4632894751907
5465167948001
41510105455501
87129547172401
468535826053501
9906293406944653501
84817574770589638001
158414167964045700001
792081397330050024751
31693914535837935570580506001
153037630649666194962091443041
271789568144429080844839251966145567
37720432662731112363293109762399994510923001
24372891567119546024482755738068603581938859649
17475503855882465390801650975421264064877668777281
23294799324276996370384838607233525168032504664077707270209
40883
889785649183modified 2026-01-28 14:51:27 created 2026-01-28 14:51:17 id 187596
field value prime_id 37624 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 13 Primality testing primV(10514) [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 4.31% primV(10514) is PRP! (11.310000 seconds) modified 2003-03-25 17:22:47 created 2003-01-07 05:25:24 id 63900
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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