81505264551807 · 233444 + 5
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: | 81505264551807 · 233444 + 5 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Triplet (3), ECPP |
| Proof-code(s): (*): | c58 : Kaiser1, NewPGen, OpenPFGW, Primo |
| Decimal Digits: | 10082 (log10 is 10081.558360648) |
| Rank (*): | 82699 (digit rank is 1) |
| Entrance Rank (*): | 60344 |
| Currently on list? (*): | no |
| Submitted: | 7/23/2012 15:27:48 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 108459 |
| Status Flags: | Verify |
| Score (*): | 32.4653 (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.
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 323
Subcategory: "ECPP"
(archival tag id 214441, tag last modified 2024-04-19 02:37:11)- Triplet (archivable class *)
- Prime on list: no, rank 27
Subcategory: "Triplet (3)"
(archival tag id 214442, tag last modified 2023-03-11 15:53:59)
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 108459 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 81505264551807 2 33444 5 2>&1 [Elapsed time: 8.182 seconds] modified 2020-07-07 22:30:25 created 2012-07-23 15:35:18 id 146501
field value prime_id 108459 person_id 9 machine Ditto P4 P4 what prp notes Command: /home/ditto/client/pfgw -tc -q"81505264551807*2^33444+5" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 81505264551807*2^33444+5 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 5+sqrt(5) Calling N-1 BLS with factored part 0.10% and helper 0.08% (0.40% proof) 81505264551807*2^33444+5 is Fermat and Lucas PRP! (42.1779s+0.0231s) [Elapsed time: 43.00 seconds] modified 2020-07-07 22:30:25 created 2012-07-23 15:38:14 id 146504
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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