(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 (*): | Proven |
| 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 (*): | 109006 (digit rank is 4) |
| Entrance Rank (*): | 19477 |
| Currently on list? (*): | yes |
| Submitted: | 1998 |
| Last modified: | 3/13/2023 06:47:08 UTC |
| Database id: | 72546 |
| Status Flags: | none |
| 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 2023-03-11 15:53:59)- Generalized Lucas Number (archivable *)
- Prime on list: no, rank 111
Subcategory: "Generalized Lucas Number"
(archival tag id 181340, tag last modified 2023-10-24 02:37:13)- Wagstaff (archivable *)
- Prime on list: yes, rank 12
Subcategory: "Wagstaff"
(archival tag id 181342, tag last modified 2023-10-24 02:37:14)
User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
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 Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1100000000004299235 -q"(2^5807+1)/3" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing (2^5807+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000004299235
Running N-1 test using base 2
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Calling N+1 BLS with factored part 39.10% and helper 7.84% (125.17% proof)
(2^5807+1)/3 is prime! (0.4264s+0.0002s)
[Elapsed time: 1.00 seconds]
Helper File:
2
5807
17419
365779
60457879
11779462459
56638102947268163
2018783289176983787
6345446910644914140703
14606763696360729501079
221290227668343044301796313
3
11
19
331
811
1033
1291
15121
87211
104491
9084611
18837001
25878691
1591582393
98047514251
2779191397441
2932031007403
15686603697451
385838642647891
28862329116475862011
2942214521663121208921
427395892287842191143360001
7758393259817509736150367811
109053678968940302364939183451
5207764094818278036298719654961
59904608378705661377430182608711698924130721
74511568294243628863306502825698825239868474219
28710288506911290785879789170591788...(96 digits)...42998599690848163865371401808988833
83861817871925183739792206470703862...(98 digits)...78546547694793573468589875745315081
47595742839030922053291102186978018...(120 digits)...39043182168427476091234134439970593modified 2023-03-13 06:47:08 created 2023-03-13 06:47:07 id 181566
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 22:30:45 created 2004-11-29 21:55:56 id 77544
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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