(V(77786, 1, 6453) + 1)/(V(77786, 1, 27) + 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(77786, 1, 6453) + 1)/(V(77786, 1, 27) + 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: | 31429 (log10 is 31428.932648348) |
| Rank (*): | 67945 (digit rank is 1) |
| Entrance Rank (*): | 47767 |
| Currently on list? (*): | short |
| Submitted: | 12/26/2012 17:13:59 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 110481 |
| Status Flags: | Verify |
| Score (*): | 35.9835 (normalized score 0.0001) |
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 4
Subcategory: "Lehmer primitive part"
(archival tag id 214827, tag last modified 2023-03-11 15:53:59)
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 110481 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"(lucasV(77786,1,6453)+1)/(lucasV(77786,1,27)+1)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] (lucasV(77786,1,....V(77786,1,27)+1) 1/1 mro=0 trial factoring to 9867605 (lucasV(77786,1,6453)+1)/(lucasV(77786,1,27)+1) has no small factor. [Elapsed time: 25.563 seconds] modified 2020-07-07 22:30:23 created 2012-12-26 17:18:01 id 151238
field value prime_id 110481 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -tc -q"(lucasV(77786,1,6453)+1)/(lucasV(77786,1,27)+1)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing (lucasV(77786,1,6453)+1)/(lucasV(77786,1,27)+1) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 59 Running N-1 test using base 109 Running N-1 test using base 113 Running N-1 test using base 151 Running N+1 test using discriminant 163, base 24+sqrt(163) Calling N-1 BLS with factored part 1.58% and helper 0.06% (4.80% proof) (lucasV(77786,1,6453)+1)/(lucasV(77786,1,27)+1) is Fermat and Lucas PRP! (819.2734s+0.0062s) [Elapsed time: 13.65 minutes] modified 2020-07-07 22:30:23 created 2012-12-26 17:23:01 id 151239
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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