p(1132288)
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(1132288) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Partitions, ECPP |
| Proof-code(s): (*): | c4 : Broadhurst, Primo |
| Decimal Digits: | 1179 (log10 is 1178.5111104753) |
| Rank (*): | 122601 (digit rank is 32) |
| Entrance Rank (*): | 40995 |
| Currently on list? (*): | no |
| Submitted: | 12/20/2000 21:19:18 UTC |
| Last modified: | 2/4/2026 10:37:15 UTC |
| Database id: | 48340 |
| Blob database id: | 41 |
| Status Flags: | none |
| Score (*): | 25.7857 (normalized score 0) |
Description: (from blob table id=41)
[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 190
Subcategory: "Partitions"
(archival tag id 177212, tag last modified 2023-03-11 15:53:59)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 1105
Subcategory: "ECPP"
(archival tag id 177211, 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 48340 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 3242870005...1875913393 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000008616999244.txt
trial
Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3915-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 3915-bit number
Running N+1 test using discriminant 13, base 4+sqrt(13)
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3915-bit number
Calling N+1 BLS with factored part 100.00% and helper 1.28% (301.35% proof)
3242870005...1875913393 is prime! (0.2753s+0.0003s)
[Elapsed time: 5.00 seconds]
Helper File:
2
7
139
15215240897
3
17
23
149
9547
423949
19728522024259778170362071
38727451627662203625883901799720658...(1138 digits)...96436827784452128288646914808612099modified 2026-02-04 10:37:15 created 2026-02-04 10:37:10 id 187701
field value prime_id 48340 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 3 Primality testing 3242870005...1875913393 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 13, base 1+sqrt(13) Running N+1 test using discriminant 13, base 4+sqrt(13) Running N+1 test using discriminant 13, base 5+sqrt(13) Running N+1 test using discriminant 13, base 6+sqrt(13) Running N+1 test using discriminant 13, base 8+sqrt(13) Running N+1 test using discriminant 13, base 10+sqrt(13) Calling N+1 BLS with factored part 0.84% and helper 0.41% (2.96% proof) 3242870005...1875913393 is Fermat and Lucas PRP! (57.370000 seconds) modified 2003-03-25 17:21:44 created 2003-02-01 06:04:46 id 68011
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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