108416458051\
3253166678679240531131941884663704319991773115000016384 + 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: | 108416458051\ 3253166678679240531131941884663704319991773115000016384 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Fermat |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | L5122 : Tennant, LLR2, PrivGfnServer, LLR |
| Decimal Digits: | 1000000 (log10 is 999999) |
| Rank (*): | 2887 (digit rank is 11) |
| Entrance Rank (*): | 822 |
| Currently on list? (*): | yes |
| Submitted: | 12/17/2020 15:32:29 UTC |
| Last modified: | 5/20/2023 20:59:19 UTC |
| Database id: | 131482 |
| Status Flags: | none |
| Score (*): | 46.633 (normalized score 4.5047) |
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 1173
Subcategory: "Generalized Fermat"
(archival tag id 225756, tag last modified 2024-11-22 05:37:10)
User comments about this prime (disclaimer):
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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 131482 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 1084164580...7731150000^16384+1 [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_file_id_131482
F: 1084164580513253....31150000^16384+1 53248/10527331 (trial factor to 394424524)
F: 1084164580513253....31150000^16384+1 96256/10527331 (trial factor to 394424524)
F: 1084164580513253....31150000^16384+1 145408/10527331 (trial factor to 394424524)
F: 1084164580513253....31150000^16384+1 200704/10527331 (trial factor to 394424524)
F: 1084164580513253....31150000^16384+1 253952/10527331 (trial factor to 394424524)
F: 1084164580513253....31150000^16384+1 303104/10527331 (trial factor to 394424524)
F: 1084164580513253....31150000^16384+1 348160/10527331 (trial factor to 394424524)
F: 1084164580513253....31150000^16384+1 401408/10527331 (trial factor to 394424524)
F: 1084164580513253....31150000^16384+1 456704/10527331 (trial factor to 394424524)
F: 1084164580513253....31150000^16384+1 499712/10527331 (trial factor to 394424524)
F: 1084164580513253....31150000^16384+1 544768/10527331 (trial factor to 394424524)
F: 1084164580513253....31150000^16384+1 595968/10527331 (trial factor to 394424524)
F: 1084164580513253....31150000^16384+1 649216/10527331 (trial factor to 394424524)
F: 1084164580513253....31150000^16384+1 706560/10527331 (trial factor to 394424524)
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 40.43%
1084164580...7731150000^16384+1 is prime! (51160.9597s+0.0164s)
[Elapsed time: 14.21 hours]
Helper file contains: "2217159475779963431,4730973644289722408155387"modified 2023-03-16 01:31:54 created 2023-03-15 11:19:13 id 181600
field value prime_id 131482 person_id 9 machine Using: Xeon (pool) 4c+4c 3.5GHz what prp notes Command: /home/caldwell/clientpool/4/pfgw64 -t -q"10841645805132531666786792405311319418846637043199917731150000^16384+1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 1084164580...7731150000^16384+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 29.51% 1084164580...7731150000^16384+1 is PRP! (25246.3978s+0.0116s) [Elapsed time: 7.01 hours] modified 2021-04-20 22:39:25 created 2020-12-17 15:41:02 id 177175
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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