(23539 + 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: | (23539 + 1)/3 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | First titanic by ECPP, generalized Lucas number, Wagstaff |
| Proof-code(s): (*): | M : Morain |
| Decimal Digits: | 1065 (log10 is 1064.8680334001) |
| Rank (*): | 125252 (digit rank is 8) |
| Entrance Rank (*): | 838 |
| Currently on list? (*): | short |
| Submitted: | 1/1/1990 05:59:59 UTC |
| Last modified: | 3/13/2023 06:45:38 UTC |
| Database id: | 54344 |
| Status Flags: | none |
| Score (*): | 25.4686 (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 Lucas Number (archivable *)
- Prime on list: no, rank 112
Subcategory: "Generalized Lucas Number"
(archival tag id 181330, tag last modified 2023-10-24 02:37:13)- * old special cases (deprecated *)
- Prime on list: no, rank 1
Subcategory: "* old special cases"
(archival tag id 181329, tag last modified 2023-03-11 15:53:59)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 1137
Subcategory: "ECPP"
(archival tag id 181331, tag last modified 2024-04-24 05:37:26)- Wagstaff (archivable *)
- Prime on list: yes, rank 13
Subcategory: "Wagstaff"
(archival tag id 181332, tag last modified 2023-10-24 02:37:14)
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 54344 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1100000000005969882 -q"(2^3539+1)/3" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing (2^3539+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000005969882
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 35.06% and helper 15.47% (120.70% proof)
(2^3539+1)/3 is prime! (0.0803s+0.0002s)
[Elapsed time: 0.00 seconds]
Helper File:
2
59
233
1103
2089
3539
3033169
39232883
2278390627
10199969089
114219291889
726533058611
768614336404564651
2305843009213693951
8899767592265771227579
754338065822803709234804940450134987
3
19
787
1049
25939
82531
87211
198073
4744297
57384289
182331128681207781784391813611
7237497065445543055003057643920459
433685074806886298028919267117655888254843
358481631294404888613030634349490904280996785041660793
175639552585373358307268617903286656284026269783398738412720155379
52971487719297043857348476822653629...(107 digits)...47370545457828497960999708594427043modified 2023-03-13 06:45:38 created 2023-03-13 06:45:36 id 181564
field value prime_id 54344 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2 Primality testing (2^3539+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 13, base 1+sqrt(13) Running N+1 test using discriminant 13, base 2+sqrt(13) Running N+1 test using discriminant 13, base 3+sqrt(13) Running N+1 test using discriminant 13, base 6+sqrt(13) Running N+1 test using discriminant 13, base 8+sqrt(13) Calling N+1 BLS with factored part 2.69% and helper 1.33% (9.44% proof) (2^3539+1)/3 is Fermat and Lucas PRP! (46.500000 seconds) modified 2003-03-25 17:23:04 created 2003-01-04 05:43:33 id 60765
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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