(25807 + 1)/3
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: | (25807 + 1)/3 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Cyclotomy, generalized Lucas number, Wagstaff |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | PM : Mihailescu |
| Decimal Digits: | 1748 (log10 is 1747.60406357) |
| Rank (*): | 105424 (digit rank is 4) |
| Entrance Rank (*): | 19478 |
| Currently on list? (*): | short |
| Submitted: | 1998 |
| Last modified: | 11/29/2004 15:55:01 CDT |
| Database id: | 72546 |
| Status Flags: | Verify |
| Score (*): | 27.0163 (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.
- Cyclotomy Proof (tolerated *)
- Prime on list: no, rank 127
Subcategory: "Cyclotomy Proof"
(archival tag id 181341, tag last modified 2019-06-27 21:50:21)- Generalized Lucas Number (archivable *)
- Prime on list: no, rank 109
Subcategory: "Generalized Lucas Number"
(archival tag id 181340, tag last modified 2022-08-07 13:37:22)- Wagstaff (archivable *)
- Prime on list: yes, rank 10
Subcategory: "Wagstaff"
(archival tag id 181342, tag last modified 2022-08-07 13:37:23)
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 72546 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"(2^5807+1)/3" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (2^5807+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 431245 Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) Reduced from FFT(768,18) to FFT(768,17) Reduced from FFT(768,17) to FFT(768,16) 11620 bit request FFT size=(768,16) Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) Reduced from FFT(768,18) to FFT(768,17) Reduced from FFT(768,17) to FFT(768,16) 11620 bit request FFT size=(768,16) Running N+1 test using discriminant 13, base 1+sqrt(13) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) Reduced from FFT(768,18) to FFT(768,17) Reduced from FFT(768,17) to FFT(768,16) 11628 bit request FFT size=(768,16) Running N+1 test using discriminant 13, base 2+sqrt(13) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) Reduced from FFT(768,18) to FFT(768,17) Reduced from FFT(768,17) to FFT(768,16) 11628 bit request FFT size=(768,16) Calling N+1 BLS with factored part 1.71% and helper 0.79% (5.94% proof) (2^5807+1)/3 is Fermat and Lucas PRP! (4.3552s+0.0003s) modified 2020-07-07 17:30:45 created 2004-11-29 15:55:56 id 77544
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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