p(1168337)
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: | p(1168337) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Partitions, ECPP |
| Proof-code(s): (*): | c4 : Broadhurst, Primo |
| Decimal Digits: | 1198 (log10 is 1197.2197126482) |
| Rank (*): | 121479 (digit rank is 26) |
| Entrance Rank (*): | 39971 |
| Currently on list? (*): | no |
| Submitted: | 12/23/2000 14:13:45 UTC |
| Last modified: | 2/4/2026 10:39:59 UTC |
| Database id: | 47289 |
| Blob database id: | 46 |
| Status Flags: | none |
| Score (*): | 25.8349 (normalized score 0) |
Description: (from blob table id=46)
[This prime has a pre-calculated decimal expansion (linked blob)]
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.
- Partitions (archivable *)
- Prime on list: no, rank 185
Subcategory: "Partitions"
(archival tag id 177193, tag last modified 2023-03-11 15:53:59)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 1099
Subcategory: "ECPP"
(archival tag id 177192, tag last modified 2026-01-31 06:37:12)
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 47289 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 1657809126...3716487661 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000008616790565.txt
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3978-bit number
Running N+1 test using discriminant 11, base 1+sqrt(11)
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3978-bit number
Running N+1 test using discriminant 11, base 3+sqrt(11)
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3978-bit number
Calling N+1 BLS with factored part 100.00% and helper 3.85% (303.85% proof)
1657809126...3716487661 is prime! (0.1650s+0.0003s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
59
16859149
50930993634863599
838959835184238179
41
73
27694773243855501653517623192837126...(1194 digits)...40694006671644249988480577566608167modified 2026-02-04 10:39:59 created 2026-02-04 10:39:54 id 187706
field value prime_id 47289 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2 Primality testing 1657809126...3716487661 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 11, base 1+sqrt(11) Calling N-1 BLS with factored part 0.35% and helper 0.30% (1.41% proof) 1657809126...3716487661 is Fermat and Lucas PRP! (12.520000 seconds) modified 2003-03-25 17:21:44 created 2003-02-01 06:07:59 id 68017
Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
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