primV(5656)
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(5656) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Lucas primitive part |
| Proof-code(s): (*): | DK : Dubner, Keller, Cruncher |
| Decimal Digits: | 1004 (log10 is 1003.1408699358) |
| Rank (*): | 136192 (digit rank is 176) |
| Entrance Rank (*): | 10073 |
| Currently on list? (*): | no |
| Submitted: | 7/1995 |
| Last modified: | 2/4/2026 10:45:34 UTC |
| Database id: | 58659 |
| Status Flags: | none |
| Score (*): | 25.2818 (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 141
Subcategory: "Lucas primitive part"
(archival tag id 195714, 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 58659 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 1383152085...9615736001 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000216934249.txt
trial
Running N-1 test using base 17
Generic modular reduction using generic reduction FMA3 FFT length 320 on A 3333-bit number
Running N-1 test using base 29
Generic modular reduction using generic reduction FMA3 FFT length 320 on A 3333-bit number
Running N+1 test using discriminant 43, base 3+sqrt(43)
Generic modular reduction using generic reduction FMA3 FFT length 320 on A 3333-bit number
Calling N-1 BLS with factored part 36.07% and helper 1.62% (109.87% proof)
1383152085...9615736001 is prime! (0.1774s+0.0003s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
23
41
47
67
101
151
331
401
409
919
1087
1103
1223
1597
1601
2161
2207
2447
3001
3041
3469
3571
4481
23663
63443
124001
570601
6376021
6996001
9125201
107420801
177736001
5738108801
66265118449
23230657239121
23725145626561
340986856708627
51793685214662401
3160438834174817356001
470039965023902754923207
562627837283291940137654881
7601587101128729489773008667804801
5474303442249842401513080472803833316281938081
43
138053
1962937049modified 2026-02-04 10:45:34 created 2026-02-04 10:45:22 id 187718
field value prime_id 58659 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 17 Primality testing primV(5656) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 29 Calling Brillhart-Lehmer-Selfridge with factored part 8.88% primV(5656) is PRP! (4.970000 seconds) modified 2003-03-25 17:22:48 created 2003-01-07 03:32:58 id 63778
Query times: 0.0004 seconds to select prime, 0.0004 seconds to seek comments.
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