(4604801 - 1)/459
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: | (4604801 - 1)/459 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Generalized repunit |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | CH5 : Kruppa, Soule, Minovic, OpenPFGW, Primo, CHG |
| Decimal Digits: | 12782 (log10 is 12781.238537218) |
| Rank (*): | 82718 (digit rank is 3) |
| Entrance Rank (*): | 27907 |
| Currently on list? (*): | no |
| Submitted: | 1/6/2006 19:11:56 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 76689 |
| Status Flags: | Verify |
| Score (*): | 33.2004 (normalized score 0) |
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 Repunit (archivable *)
- Prime on list: no, rank 75
Subcategory: "Generalized Repunit"
(archival tag id 193582, tag last modified 2025-09-11 16:37:14)
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 76689 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -tc -q"(460^4801-1)/459" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (460^4801-1)/459 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(5120,21) to FFT(5120,20) Reduced from FFT(5120,20) to FFT(5120,19) Reduced from FFT(5120,19) to FFT(5120,18) Reduced from FFT(5120,18) to FFT(5120,17) 84926 bit request FFT size=(5120,17) Running N+1 test using discriminant 17, base 3+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(5120,21) to FFT(5120,20) Reduced from FFT(5120,20) to FFT(5120,19) Reduced from FFT(5120,19) to FFT(5120,18) Reduced from FFT(5120,18) to FFT(5120,17) 84934 bit request FFT size=(5120,17) Calling N-1 BLS with factored part 1.34% and helper 0.07% (4.08% proof) (460^4801-1)/459 is Fermat and Lucas PRP! (180.8141s+0.0009s) [Elapsed time: 181 seconds] modified 2020-07-07 22:30:43 created 2006-01-06 19:20:54 id 82352
field value prime_id 76689 person_id 9 machine Linux P4 2.8GHz what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"(460^4801-1)/459" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 3745457 (460^4801-1)/459 has no small factor. [Elapsed time: 5.608 seconds] modified 2020-07-07 22:30:43 created 2006-01-06 19:22:01 id 82353
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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