V(7741)
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(7741) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Lucas number |
| Proof-code(s): (*): | DK : Dubner, Keller, Cruncher |
| Decimal Digits: | 1618 (log10 is 1617.7733231751) |
| Rank (*): | 108723 (digit rank is 1) |
| Entrance Rank (*): | 4481 |
| Currently on list? (*): | no |
| Submitted: | 3/4/1995 05:59:59 UTC |
| Last modified: | 3/13/2023 06:46:25 UTC |
| Database id: | 38556 |
| Status Flags: | none |
| Score (*): | 26.7754 (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.
- Lucas Number (archivable *)
- Prime on list: no, rank 21
Subcategory: "Lucas Number"
(archival tag id 179794, tag last modified 2023-12-16 03:37:32)
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 38556 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1000000000014257765 -q"V(7741)" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing V(7741) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1000000000014257765
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 34.69% and helper 15.80% (119.91% proof)
V(7741) is prime! (0.7982s+0.0013s)
[Elapsed time: 1.00 seconds]
Helper File:
2
5
11
13
17
19
31
61
97
157
181
257
431
541
773
1291
1549
1721
5417
6709
7741
8513
46441
69677
109441
116101
144481
152629
221201
308311
719821
2564521
6168709
16586821
17861341
19148761
19856971
39639893
354391381
433494437
2607553541
6907621433
7409656801
7998082133
14279673833
691419023311
761882591401
1266715025281
66163448516461
77149788383093
92180471494753
240987583419301
86508852219867151
497882131309853461
72070039273446428491
72846749180048315217661
67712817361580804952011621
1594403967069207665025028111
38074001361639245985686714500108609
9159411196439308397478462543930769648261
28184229448040590408512793395201731274978795984709
3
29
41
107
2521
4643
5531
94427
546961
7772507
9793631
599786069
1720303369
6906432961
10783342081
73254041816089
258422401920467
32361122672259149
313195711516578281
39748438741079056643
15327015737936733639089
467177823226901502121899227865934545048285100074539649060171115392823339modified 2023-03-13 06:46:25 created 2023-03-13 06:46:24 id 181565
field value prime_id 38556 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 3 Primality testing V(7741) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N-1 BLS with factored part 5.75% and helper 1.40% (18.65% proof) V(7741) is Fermat and Lucas PRP! (29.780000 seconds) modified 2003-03-25 17:23:00 created 2003-01-04 17:38:16 id 61396
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.