243 · 2495732 + 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: | 243 · 2495732 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Divides Fermat F(495728), GF(495726,3), GF(495728,6), GF(495727,12) |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | L165 : Keiser, NewPGen, OpenPFGW, LLR |
| Decimal Digits: | 149233 (log10 is 149232.58741677) |
| Rank (*): | 41435 (digit rank is 1) |
| Entrance Rank (*): | 976 |
| Currently on list? (*): | no |
| Submitted: | 5/29/2007 19:02:13 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 80777 |
| Status Flags: | none |
| Score (*): | 40.7872 (normalized score 0.015) |
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 Divisors (bases 3,5,6,10,12) (archivable *)
- Prime on list: no, rank 34, weight 46.280261849047
Subcategory: "Divides GF(*,12)"
(archival tag id 187409, tag last modified 2024-04-07 12:37:28)- Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
- Prime on list: no, rank 35, weight 46.280261849047
Subcategory: "Divides GF(*,6)"
(archival tag id 187408, tag last modified 2023-03-31 01:37:05)- Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
- Prime on list: no, rank 42, weight 46.280261849047
Subcategory: "Divides GF(*,3)"
(archival tag id 187407, tag last modified 2024-03-22 08:37:11)- Fermat Divisors (archivable *)
- Prime on list: no, rank 24, weight 46.280261849047
Subcategory: "Divides Fermat"
(archival tag id 187406, tag last modified 2023-07-28 18:37:27)
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 80777 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -t -q"243*2^495732+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 243*2^495732+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 991488 bit request FFT size=(65536,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 243*2^495732+1 is prime! (1345.7600s+0.0000s) [Elapsed time: 1352 seconds] modified 2020-07-07 22:30:41 created 2007-05-29 19:04:36 id 90665
field value prime_id 80777 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/TrialDiv/TrialDiv -q 243 2 495732 1 2>&1 [Elapsed time: 9.425 seconds] modified 2020-07-07 22:30:41 created 2007-05-29 19:22:02 id 90666
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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