V(10691)
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(10691) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Lucas number |
| Proof-code(s): (*): | DK : Dubner, Keller, Cruncher |
| Decimal Digits: | 2235 (log10 is 2234.2868619125) |
| Rank (*): | 103391 (digit rank is 2) |
| Entrance Rank (*): | 4328 |
| Currently on list? (*): | short |
| Submitted: | 1/1/1996 05:59:59 UTC |
| Last modified: | 3/13/2023 06:18:10 UTC |
| Database id: | 33290 |
| Status Flags: | none |
| Score (*): | 27.7825 (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: yes, rank 19
Subcategory: "Lucas Number"
(archival tag id 179788, 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 33290 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1000000000014260715 -q"V(10691)" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing V(10691) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1000000000014260715
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 6+sqrt(7)
Calling N+1 BLS with factored part 29.52% and helper 22.93% (111.49% proof)
V(10691) is prime! (1.3362s+0.0077s)
[Elapsed time: 2.00 seconds]
Helper File:
2
3
11
43
107
307
1187
7129
10691
55589
74831
2501461
11128427
45887689
95696963
261399601
423834443
1828620361
11166702227
39697026371
58652142121
104258351341
108735430241
2320341157991
2615782280801
6782976947987
1076312899454363
1612441605398891
16462505459608163
700973868176383360918693381
17122083601040322581129728426619631481
38325527459198873328212646962885771219
4859308548999344216537093035272804372511
791553638726359079413274595228907780197913614784512051280040229644178119
2247476135266843338551314212819670174605190863710514854417657855649541786649
5
17
19
53
89
109
197
199
593
991
2137
2179
2269
3079
4157
4373
5779
9901
19441
19801
26731
59779
1513909
3341251
34294591
62650261
64488797
98968021
220862269
1360418597
5381132201
11806817419
18546805133
448607550257
1369471729429
2566277844349
26079400881401671
137096217949680001
1713843517309859431
61927940138475041929
12369243068750242280033
16000411124306403070561
275363930639344038915061
22584391375996021505485861
120074026624398979403194983601
25918811723998168438369194036868879
703090864493996770254757857883743257
31586676759675537868485273401584431460671718181218266739
78055008157454324226890192867523537760880343204384546349
25907092914898969940691437369938921...(90 digits)...75200737598051692209715422282187741modified 2023-03-13 06:18:10 created 2023-03-13 06:18:08 id 181561
field value prime_id 33290 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(10691) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 6+sqrt(7) Calling N+1 BLS with factored part 3.00% and helper 1.37% (10.40% proof) V(10691) is Fermat and Lucas PRP! (61.400000 seconds) modified 2003-03-25 17:22:59 created 2003-01-04 19:20:40 id 61650
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.