U(641, - 642, 2161)
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: | U(641, - 642, 2161) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Lucas number |
| Proof-code(s): (*): | x25 : Broadhurst, Water, OpenPFGW, Primo |
| Decimal Digits: | 6065 (log10 is 6064.27498468) |
| Rank (*): | 92412 (digit rank is 2) |
| Entrance Rank (*): | 27528 |
| Currently on list? (*): | no |
| Submitted: | 12/5/2003 08:18:40 UTC |
| Last modified: | 2/4/2026 12:20:22 UTC |
| Database id: | 67550 |
| Status Flags: | none |
| Score (*): | 30.8885 (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.
- Generalized Lucas Number (archivable *)
- Prime on list: no, rank 83
Subcategory: "Generalized Lucas Number"
(archival tag id 194888, tag last modified 2025-10-27 15:37:13)
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 67550 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper_1100000001196947036.txt -q"lucasU(641,-642,2161)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing lucasU(641,-642,2161) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000001196947036.txt
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 2K on A 20146-bit number
Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 2K on A 20146-bit number
Running N-1 test using base 7
Generic modular reduction using generic reduction FMA3 FFT length 2K on A 20146-bit number
Running N+1 test using discriminant 19, base 15+sqrt(19)
Generic modular reduction using generic reduction FMA3 FFT length 2K on A 20146-bit number
Calling N-1 BLS with factored part 67.45% and helper 0.19% (202.53% proof)
lucasU(641,-642,2161) is prime! (5.7851s+0.0004s)
[Elapsed time: 10.00 seconds]
Helper File:
2
3
5
7
11
13
17
19
31
37
41
61
73
101
107
109
151
181
193
241
257
271
373
433
541
571
577
631
641
1021
2161
3457
3889
6481
7873
9829
17713
21121
23041
29401
58789
71713
89083
127681
169501
265141
306871
412561
412807
565111
642241
2032021
4267201
7453891
14429521
21936961
28263601
73192681
249346621
397445509
2527130371
3469024513
4143394217
6066628597
16054057153
114084603793
169614965131
450109192921
785986951051
1382390242609
3636628730929
6914773409329
20387125387621
174062126618209
753227330011813
1288493131407841
3661184307740671
3685161843750403
9021521548819411
107210511354227401
191526866034070663
191678218304244481
194612749335727553
458663297922115201
487236793017288961
2421723353067622321
3665556965080124977
10296663444023513239
16994512979906259169
179694205614453024577
301484271154883895721
1747318086953983666081
2597149573224016416913
4137287227711918692481
5771771993668057198121
72306057847196424008071
705483366154857713042857
673075662947837054115611617
1250119294775874565973414191
1815793510662698804920099441
4513480338561590791384210321
6981790811626213010832817921
9018558850941415096814957881
860144110755894443602791716761
132500834273991696420129006919789
4180978533797943284836611261673921
167119503213022609015990518463401841
298080951588868759136350686128459761
5558811318818975260322475405931254241
11649754143433418685764671923334564140884393569
2326947978249146336329780563522283500929926073269858321
36862050775886530781281783827896540636147250556815985099859377
24034808822211607756213534922103688063156036069390673154751477142521
4175002938173140249285821174170164374512903542550221688759673096990272791
1278464668254826150734324915865712004277339508829117990629580221238507980821
89946303566182695792180941419732681...(129 digits)...04946325757963770237799389853610881
11826947385776516436126482217735701...(142 digits)...84879991736962633061692512297519921
12629802636810798273410753955833806...(194 digits)...32750693606610436926903037740804641
18969433683492901536178060920680476...(195 digits)...33239999160568560359311716029907801
51489736954864659270220553368442386...(266 digits)...66167653990466318909512783715491761
62950575454633588417779827118592906...(1610 digits)...16921060697255872351611775807116481
27481
3502117modified 2026-02-04 12:20:22 created 2026-02-04 12:20:12 id 187748
field value prime_id 67550 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"lucasU(641,-642,2161)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing lucasU(641,-642,2161) [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 1671974 Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2560,21) to FFT(2560,20) Reduced from FFT(2560,20) to FFT(2560,19) Reduced from FFT(2560,19) to FFT(2560,18) Reduced from FFT(2560,18) to FFT(2560,17) Reduced from FFT(2560,17) to FFT(2560,16) 40300 bit request FFT size=(2560,16) Running N+1 test using discriminant 7, base 1+sqrt(7) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(2560,21) to FFT(2560,20) Reduced from FFT(2560,20) to FFT(2560,19) Reduced from FFT(2560,19) to FFT(2560,18) Reduced from FFT(2560,18) to FFT(2560,17) Reduced from FFT(2560,17) to FFT(2560,16) 40308 bit request FFT size=(2560,16) Calling N-1 BLS with factored part 2.58% and helper 0.08% (7.81% proof) lucasU(641,-642,2161) is Fermat and Lucas PRP! (31.6889s+0.0016s) modified 2020-07-07 22:30:47 created 2003-12-05 08:27:07 id 72486
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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