1381595338887690358821474589959638055848096769928148782339849168699728696005036217596639028980911635464344630906955931847649826418753025466730960\
47093511481998019892105889132464543550102310865144\
502037206654116795191514099734330521220120978407024096 + 1
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: | 1381595338887690358821474589959638055848096769928148782339849168699728696005036217596639028980911635464344630906955931847649826418753025466730960\ 47093511481998019892105889132464543550102310865144\ 502037206654116795191514099734330521220120978407024096 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Fermat |
| Unofficial Comments: | This prime has 2 user comments below. |
| Proof-code(s): (*): | p417 : Tennant, LLR2, PrivGfnServer, OpenPFGW |
| Decimal Digits: | 1000000 (log10 is 999999) |
| Rank (*): | 2668 (digit rank is 19) |
| Entrance Rank (*): | 1080 |
| Currently on list? (*): | short |
| Submitted: | 8/3/2021 12:15:53 UTC |
| Last modified: | 5/20/2023 20:59:19 UTC |
| Database id: | 132584 |
| Status Flags: | none |
| Score (*): | 46.633 (normalized score 5.1969) |
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.
- Generalized Fermat (archivable *)
- Prime on list: no, rank 1042
Subcategory: "Generalized Fermat"
(archival tag id 226240, tag last modified 2024-04-24 19:37:19)
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 132584 person_id 9 machine Using: Digital Ocean Droplet what prime notes PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 1381595338...2097840702^4096+1 [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.txt
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 86.10%
1381595338...2097840702^4096+1 is prime! (44222.5728s+0.0360s)
[Elapsed time: 12.28 hours]
Helper File:
2
3
11
3319
39002209166721466412601474313
16171133571763479876871584838167225...(211 digits)...90783089470092989022566928882860401modified 2023-03-14 02:49:16 created 2023-03-13 14:32:13 id 181582
field value prime_id 132584 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prp notes PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 1381595338...2097840702^4096+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N-1 test using base 7 Running N-1 test using base 23 Running N-1 test using base 29 Running N-1 test using base 37 Calling Brillhart-Lehmer-Selfridge with factored part 2.19% 1381595338...2097840702^4096+1 is PRP! (125799.0939s+0.0117s) [Elapsed time: 34.94 hours] modified 2022-07-11 18:21:46 created 2021-08-03 12:16:01 id 178296
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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