U(2729, - 2730, 1801)
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(2729, - 2730, 1801) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Lucas number |
| Proof-code(s): (*): | x25 : Broadhurst, Water, OpenPFGW, Primo |
| Decimal Digits: | 6186 (log10 is 6185.09260562) |
| Rank (*): | 92223 (digit rank is 8) |
| Entrance Rank (*): | 27064 |
| Currently on list? (*): | no |
| Submitted: | 11/17/2003 08:13:08 UTC |
| Last modified: | 2/4/2026 12:20:11 UTC |
| Database id: | 67233 |
| Status Flags: | none |
| Score (*): | 30.9497 (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 82
Subcategory: "Generalized Lucas Number"
(archival tag id 194864, 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 67233 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper_1100000001878594659.txt -q"lucasU(2729,-2730,1801)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing lucasU(2729,-2730,1801) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000001878594659.txt
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 2K on A 20547-bit number
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction FMA3 FFT length 2K on A 20547-bit number
Calling N-1 BLS with factored part 48.16% and helper 0.25% (144.73% proof)
lucasU(2729,-2730,1801) is prime! (9.7189s+0.0003s)
[Elapsed time: 10.00 seconds]
Helper File:
2
3
5
7
11
13
19
31
37
41
61
73
101
113
137
151
181
229
241
307
401
521
601
701
821
1033
1171
1429
1621
1801
2521
2729
3001
4441
4451
4951
6301
6841
9391
14401
22501
25111
26881
27793
29881
33769
35401
57601
87649
94951
129097
199741
202201
344863
385831
709381
1491601
2833241
3154321
4696651
7450171
7452901
7455631
10038241
15147577
17377201
24539681
29505781
139475683
217065601
252335701
290033281
1499030101
9668052721
12280979521
53953395823
194569191181
1003473511861
1792453944601
6725133069901
16759333385101
32907816327241
410171684485501
478940070276433
1223288966139301
10829557014075601
153140142914979001
367485465422499031
104528555861146762291
13013939518714393894081
26128179526226066016001
35200935934043256424849
48643098778557485009641
583228942754449950492701
9721064466867963345316566401
33761123666041660178928558030433
6307928655005944160400543282595891
23724696231025016423470765233081301
23810579068940595587378854950283614451
171376695506573539304218199636262111000001
3999191875372696962453904169274880118419026373561
318571766269462871359429153060499959763038915833421
1784716102340700891049290090827789697903459470911547834262301
22658568232785909380012223986611117329028669926731651256854041
169463951364646893947539856736285287759486750904305291787577351
11267622898083476833180892685847195878994633390594164482885865781384109180821
25719354448156567241366867421388679...(136 digits)...19193543400107494342397638594048521
10507020377365227024220065909820682...(1642 digits)...84805258941051650095401343670294401
283
1777
8419
399059modified 2026-02-04 12:20:11 created 2026-02-04 12:20:01 id 187747
field value prime_id 67233 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"lucasU(2729,-2730,1801)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing lucasU(2729,-2730,1801) [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 1708090 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) 41102 bit request FFT size=(2560,17) 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) 41110 bit request FFT size=(2560,17) Calling N-1 BLS with factored part 2.96% and helper 0.25% (9.15% proof) lucasU(2729,-2730,1801) is Fermat and Lucas PRP! (35.0611s+0.0103s) modified 2020-07-07 22:30:47 created 2003-11-17 08:23:01 id 72165
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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