(V(45366, 1, 4857) + 1)/(V(45366, 1, 3) + 1)
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: | (V(45366, 1, 4857) + 1)/(V(45366, 1, 3) + 1) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Lehmer primitive part |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | x25 : Broadhurst, Water, OpenPFGW, Primo |
| Decimal Digits: | 22604 (log10 is 22603.769789892) |
| Rank (*): | 72509 (digit rank is 1) |
| Entrance Rank (*): | 52666 |
| Currently on list? (*): | short |
| Submitted: | 2/5/2013 22:45:44 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 111121 |
| Status Flags: | Verify |
| Score (*): | 34.9647 (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.
- Lehmer primitive part (archivable *)
- Prime on list: yes, rank 8
Subcategory: "Lehmer primitive part"
(archival tag id 215067, tag last modified 2023-03-11 15:53:59)
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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 111121 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"(lucasV(45366,1,4857)+1)/(lucasV(45366,1,3)+1)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] (lucasV(45366,1,....sV(45366,1,3)+1) 1/1 mro=0 trial factoring to 6923599 (lucasV(45366,1,4857)+1)/(lucasV(45366,1,3)+1) has no small factor. [Elapsed time: 13.265 seconds] modified 2020-07-07 22:30:23 created 2013-02-05 22:48:01 id 152516
field value prime_id 111121 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -tc -q"(lucasV(45366,1,4857)+1)/(lucasV(45366,1,3)+1)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing (lucasV(45366,1,4857)+1)/(lucasV(45366,1,3)+1) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 29 Running N+1 test using discriminant 47, base 18+sqrt(47) Calling N-1 BLS with factored part 0.97% and helper 0.03% (2.93% proof) (lucasV(45366,1,4857)+1)/(lucasV(45366,1,3)+1) is Fermat and Lucas PRP! (200.7965s+0.0039s) [Elapsed time: 3.33 minutes] modified 2020-07-07 22:30:23 created 2013-02-05 22:53:01 id 152517
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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