p(158381443)
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(158381443) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Partitions,ECPP |
| Proof-code(s): (*): | E1 : Batalov, CM |
| Decimal Digits: | 14011 (log10 is 14010.723632422) |
| Rank (*): | 82140 (digit rank is 1) |
| Entrance Rank (*): | 82048 |
| Currently on list? (*): | yes |
| Submitted: | 5/12/2026 17:31:18 UTC |
| Last modified: | 5/14/2026 23:37:16 UTC |
| Database id: | 142241 |
| Status Flags: | Verify |
| Score (*): | 33.4848 (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.
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 235
Subcategory: "ECPP"
(archival tag id 240276, tag last modified 2026-07-01 20:37:10)- Partitions (archivable *)
- Prime on list: yes, rank 17
Subcategory: "Partitions"
(archival tag id 240277, tag last modified 2026-05-22 15:37:14)
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 142241 person_id 9 machine Using: Digital Ocean Droplet what prp notes PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 5292153366...3748929113 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial
Running N-1 test using base 5
Generic modular reduction using generic reduction FMA3 FFT length 5K on A 46543-bit number
Running N-1 test using base 11
Generic modular reduction using generic reduction FMA3 FFT length 5K on A 46543-bit number
Running N+1 test using discriminant 17, base 2+sqrt(17)
Generic modular reduction using generic reduction FMA3 FFT length 5K on A 46543-bit number
Calling N+1 BLS with factored part 0.05% and helper 0.03% (0.18% proof)
5292153366...3748929113 is Fermat and Lucas PRP! (17.1468s+0.0030s)
[Elapsed time: 20.00 seconds]modified 2026-05-14 23:31:38 created 2026-05-14 23:01:12 id 188427
Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.