primV(9072)
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(9072) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Lucas primitive part |
| Proof-code(s): (*): | DK : Dubner, Keller, Cruncher |
| Decimal Digits: | 1084 (log10 is 1083.3919270559) |
| Rank (*): | 127591 (digit rank is 18) |
| Entrance Rank (*): | 9074 |
| Currently on list? (*): | no |
| Submitted: | 7/1995 |
| Last modified: | 2/4/2026 10:42:24 UTC |
| Database id: | 53176 |
| Status Flags: | none |
| Score (*): | 25.5225 (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 139
Subcategory: "Lucas primitive part"
(archival tag id 195712, 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 53176 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 2465625175...4794096641 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000305924281.txt
trial
Running N-1 test using base 13
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3599-bit number
Running N-1 test using base 43
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3599-bit number
Running N+1 test using discriminant 59, base 4+sqrt(59)
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3599-bit number
Calling N-1 BLS with factored part 62.81% and helper 2.20% (190.72% proof)
2465625175...4794096641 is prime! (0.1406s+0.0003s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
17
19
23
47
53
107
109
127
383
647
769
863
1087
1103
2207
2269
3023
3079
3167
4373
4481
5779
6263
19009
19441
19583
68687
103681
270143
5662847
6803327
8982143
11128427
62650261
447901921
1828620361
10749957121
12340209383
16093237249
19073614849
177962167367
186812208641
6782976947987
11862575248703
25033626656641
48265838239823
303039789569567
1145496371382309889
115561578124838522881
742078633406435412481
1985848125630403202878453557046838544871227168001
26628225786384293012386130857533544...(155 digits)...01681114097670875635975132400705663
5827
591131
158600542496857modified 2026-02-04 10:42:24 created 2026-02-04 10:42:14 id 187712
field value prime_id 53176 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(9072) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 43 Calling Brillhart-Lehmer-Selfridge with factored part 13.31% primV(9072) is PRP! (6.700000 seconds) modified 2003-03-25 17:22:48 created 2003-01-07 04:33:51 id 63808
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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