V(14449)

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(14449)
Verification status (*):Proven
Official Comment (*):Lucas number
Proof-code(s): (*):DK : Dubner, Keller, Cruncher
Decimal Digits:3020   (log10 is 3019.6624139719)
Rank (*):95743 (digit rank is 9)
Entrance Rank (*):1840
Currently on list? (*):short
Submitted:3/4/1995 05:59:59 UTC
Last modified:3/13/2023 06:47:59 UTC
Database id:29473
Status Flags:none
Score (*):28.7208 (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 16
Subcategory: "Lucas Number"
(archival tag id 179782, 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.
fieldvalue
prime_id29473
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1000000000014264473 -q"V(14449)" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing V(14449) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1000000000014264473
Running N-1 test using base 11
Running N-1 test using base 17
Running N-1 test using base 19
Running N-1 test using base 37
Running N+1 test using discriminant 43, base 3+sqrt(43)
Calling N-1 BLS with factored part 86.04% and helper 16.82% (274.97% proof)


V(14449) is prime! (2.1379s+0.0013s)
[Elapsed time: 2.00 seconds]


Helper File:
2
3
5
7
13
23
29
83
167
211
257
281
421
577
1427
1597
1733
3001
5417
6709
8513
9521
14449
14503
98837
131063
144481
308311
469561
1765063
7772507
39639893
52815601
65740583
101232653
433494437
2271505531
3415914041
7842533329
43454865523
106205194357
761882591401
39488879317091
73254041816089
258422401920467
1050474234583201
1790970787001003
2494887570160189
40304542927511801
313195711516578281
3171921919597295201
127388122711994872307
3120953454094204326361
4054772314921127946721
187209728806728571172807
689529693448123842995171
14187954345303564388390001
658078658277725444483848541
16726927264752630059929432849
24223150519504550429014816961
10112992306285268138636226624093401
126117711915911646784404045944033521
2706625868504399192497293155270920561
47790778426343969958962381134866119329
2937770553714972466120415196422294608482890627
63806927452714047340778156846369278969435365966728521
1395074096859278363190191555545971276908614124827098908595241385861764117244912701909
40562861651727393227582583755423301101005117367388908136217315748721528533733846677861
18555662465631663373452028620745466...(91 digits)...91954025909031615085668633005987161
14355757549936931384866709730761639...(97 digits)...61686903314393269927573114236177851
58941887581004881636880688874515745...(142 digits)...14773089829964605386287839603534181
34385514254915907786172564989625930...(158 digits)...61478748128762180993582853230027127
78120130459917162223161859417221427...(1137 digits)...13194402621723303109817658645221001
11
47
101
151
1103
2063
3571
4129
14447
28901
51001
167621
187823
332303
635801
895901
1158551
2968201
6271301
9303823
12760031
878516651
1261615051
1598863841
2224201801
2731729151
10745088481
87314913167
1371955936801
109627772701961
266153420920351
115613939510481515041
1627727616354246028751
22054919149909719709751
402673930676045499545381
176823816609591734343958261
20814129394254998922667272063601
219058706154953684854972551550917073740147901
795954394282744053474161101150396077552743674481
150576932198503649676909813176623720784127489057150620374087531885751
modified2023-03-13 06:47:59
created2023-03-13 06:47:57
id181567

fieldvalue
prime_id29473
person_id9
machineLinux PII 200
whatprp
notesPFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 11 Primality testing V(14449) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 17, base 6+sqrt(17) Calling N-1 BLS with factored part 2.98% and helper 1.84% (10.81% proof) V(14449) is Fermat and Lucas PRP! (123.100000 seconds)
modified2003-03-25 17:22:57
created2003-01-04 21:55:45
id61884

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
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