11754128376394782080351\
49360635999371658705159870633484377238553812244526\
118442328862282459012925328173493478126787295998648192 + 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: | 11754128376394782080351\ 49360635999371658705159870633484377238553812244526\ 118442328862282459012925328173493478126787295998648192 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Fermat |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | L5749 : Gahan, LLR2, LLR |
| Decimal Digits: | 1000000 (log10 is 999999) |
| Rank (*): | 2869 (digit rank is 12) |
| Entrance Rank (*): | 2117 |
| Currently on list? (*): | short |
| Submitted: | 6/2/2023 12:38:30 UTC |
| Last modified: | 6/7/2023 04:17:35 UTC |
| Database id: | 136122 |
| Status Flags: | none |
| Score (*): | 46.633 (normalized score 4.5827) |
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 1162
Subcategory: "Generalized Fermat"
(archival tag id 228608, tag last modified 2024-10-29 10:37:19)
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 136122 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 1175412837...8729599864^8192+1 [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file p_136122
trial
Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 336K, Pass1=448, Pass2=768, clm=4 on A 3321925-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 99.26%
1175412837...8729599864^8192+1 is prime! (27502.1942s+0.0162s)
[Elapsed time: 7.64 hours]
Helper File:
14692660470493477600439367007949992...(122 digits)...30737661566602168668476584841199983modified 2023-06-07 04:17:35 created 2023-06-06 20:39:13 id 181970
field value prime_id 136122 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 1175412837...8729599864^8192+1 [N-1, Brillhart-Lehmer-Selfridge]
trial
Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 336K, Pass1=448, Pass2=768, clm=4 on A 3321925-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.74%
1175412837...8729599864^8192+1 is PRP! (30048.3221s+0.0103s)
[Elapsed time: 8.35 hours]modified 2023-06-03 12:52:03 created 2023-06-03 04:31:15 id 181952
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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