p(80036992)
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(80036992) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Partitions, ECPP |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | c46 : Boncompagni, Primo |
| Decimal Digits: | 9958 (log10 is 9957.5555772841) |
| Rank (*): | 86624 (digit rank is 1) |
| Entrance Rank (*): | 55633 |
| Currently on list? (*): | no |
| Submitted: | 11/2/2011 18:34:27 UTC |
| Last modified: | 2/4/2026 12:20:43 UTC |
| Database id: | 102651 |
| Blob database id: | 273 |
| Status Flags: | Verify |
| Score (*): | 32.4269 (normalized score 0) |
Description: (from blob table id=273)
Certificate
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 373
Subcategory: "ECPP"
(archival tag id 213578, tag last modified 2026-01-31 06:37:12)- Partitions (archivable *)
- Prime on list: no, rank 56
Subcategory: "Partitions"
(archival tag id 213579, tag last modified 2023-03-11 15:53:59)
User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
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 102651 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 3593815394...2143262381 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000537314300.txt
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 3K on A 33079-bit number
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction FMA3 FFT length 3K on A 33079-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 153/33185 ERROR: ROUND OFF 0.45312>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction FMA3 FFT length 4K on A 33079-bit number
Calling N-1 BLS with factored part 0.21% and helper 0.17% (0.79% proof)
3593815394...2143262381 is Fermat and Lucas PRP! (6.1947s+0.0015s)
[Elapsed time: 10.00 seconds]
Helper File:
2
3
5
157
36792737
872228317
7
19
15032999
30274213modified 2026-02-04 12:20:43 created 2026-02-04 12:20:33 id 187750
field value prime_id 102651 person_id 9 machine Ditto P4 P4 what trial_divided notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 3593815394917215....4931992143262381 1/1 mro=0 trial factoring to 2860193 3593815394...2143262381 has no small factor. [Elapsed time: 11.982 seconds] modified 2020-07-07 22:30:30 created 2011-11-02 18:35:01 id 134893
field value prime_id 102651 person_id 9 machine Ditto P4 P4 what prp notes PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 3593815394...2143262381 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N-1 BLS with factored part 0.04% and helper 0.02% (0.14% proof) 3593815394...2143262381 is Fermat and Lucas PRP! (39.4627s+0.0033s) [Elapsed time: 39.00 seconds] modified 2020-07-07 22:30:30 created 2011-11-02 18:38:02 id 134894
Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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