primV(5414)
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(5414) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Lucas primitive part |
| Proof-code(s): (*): | DK : Dubner, Keller, Cruncher |
| Decimal Digits: | 1131 (log10 is 1130.9819630587) |
| Rank (*): | 125291 (digit rank is 4) |
| Entrance Rank (*): | 8601 |
| Currently on list? (*): | no |
| Submitted: | 7/1995 |
| Last modified: | 2/4/2026 10:38:06 UTC |
| Database id: | 50989 |
| Status Flags: | none |
| Score (*): | 25.657 (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 134
Subcategory: "Lucas primitive part"
(archival tag id 195707, 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 50989 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 9593190278...8334038281 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000001138535.txt
trial
Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3758-bit number
Running N-1 test using base 7
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3758-bit number
Running N+1 test using discriminant 13, base 1+sqrt(13)
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3758-bit number
Calling N-1 BLS with factored part 100.00% and helper 7.27% (307.27% proof)
9593190278...8334038281 is prime! (0.2113s+0.0003s)
[Elapsed time: 5.00 seconds]
Helper File:
2
5
89
199
2707
2789
8123
9901
19801
59369
771781
855997
928157
4274579
4767481
9155747
212741833
370248451
970100381
7188487771
7374580621
35723340241
1436799870283
2595961660051
795047201679721
798982537859791
1387699497662809
68541957733949701
368223917042218483
26941121419798939189
1027729298220237292846693
5395243337012494775921359
8399194089571232622081529
12908565561241046084389765964009
118460891109174497087747370851033
12365376343954471620209963483487121
79294907482525831172666228553046708561
2506276073966449566236588671749053615207753
298038128343372140803800046612728161434819831
666146992336447094037882680026427177876016818933
37600201367652288450451847693675279760013472846415544221967071958610209
109232638627806347309681912620627250266978342009136080838571332708783591
14796476495996801429563728784123342586487392199590707964325171434039716141
101814304324334006347720247956531431054730671614952768502158077738161907507
56909671435221082533169582520085662884377962564222829999842181652894123123019
83412776666668340974605642866717361170696909170976578943224886346525020926392657448369
50221617492347410835001189762529438377673186530427303161494399851009900695146062023971609
3
7
43
163
307
21649
800483
261399601
332423249
350207569
23515719083
67031206681
287610766185159143modified 2026-02-04 10:38:06 created 2026-02-04 10:37:56 id 187704
field value prime_id 50989 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 3 Primality testing primV(5414) [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 2.61% primV(5414) is PRP! (3.200000 seconds) modified 2003-03-25 17:22:48 created 2003-01-07 04:35:39 id 63817
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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