U(113, - 114, 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(113, - 114, 1801) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Lucas number |
| Proof-code(s): (*): | x25 : Broadhurst, Water, OpenPFGW, Primo |
| Decimal Digits: | 3703 (log10 is 3702.4249394166) |
| Rank (*): | 97640 (digit rank is 1) |
| Entrance Rank (*): | 24841 |
| Currently on list? (*): | no |
| Submitted: | 10/23/2001 22:12:49 UTC |
| Last modified: | 2/4/2026 11:22:13 UTC |
| Database id: | 27787 |
| Status Flags: | none |
| Score (*): | 29.3551 (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 102
Subcategory: "Generalized Lucas Number"
(archival tag id 179765, 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 27787 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper_1100000000696698421.txt -q"lucasU(113,-114,1801)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing lucasU(113,-114,1801) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000696698421.txt
trial
Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 1280 on A 12300-bit number
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction FMA3 FFT length 1280 on A 12300-bit number
Calling N-1 BLS with factored part 35.74% and helper 0.02% (107.24% proof)
lucasU(113,-114,1801) is prime! (1.1539s+0.0003s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
19
31
37
41
61
73
101
113
151
181
317
401
461
601
631
751
991
1201
1361
1801
1873
1931
2221
4861
10501
17341
21751
31489
33601
55333
60661
124097
184351
205651
238591
263101
1752721
2790901
6683401
8627701
29751031
35847601
38883001
83405701
168883021
190730791
225041581
812651293
868818751
3478564351
3676739401
5764233781
50992972501
79434080281
88397331361
210536307061
427480842421
533823090001
725300003971
905899331569
1375556783329
2453692022101
9486592199761
35395636038421
81174840687001
156219096288811
1602497812489201
213906023473058321
738001271892523801
22991182928413917361
87071093557665297517
91419184673863348501
334361836439352439801
51258798907783619533201
282637818251508659492251
27491780933861915031954001
208449087631267404075710041
2360541597469565882557526641
142211818158317330984216276671
15929492541024293827955482884891901
887844701228901652249267790583176401
1851999033697950204652658664777350701
16874771826394886067713243096458422049
272148314280023692924691861747670057001
3563612143222056557269610810959857677140351
10198899157675070020502145722605103642158378501
9937174420853503274782190412176167161443751332068968001
377783038412383401154841262652638711725637418365010360967041
18888351385778069743576499789491982525516211171371106185382858105240075599851699201
22263357571667733409157239261865045...(150 digits)...97471636798834594070307675409789201modified 2026-02-04 11:22:13 created 2026-02-04 11:22:08 id 187727
field value prime_id 27787 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Reading factors from helper file helper Running N-1 test using base 2 Primality testing U(113,-114,1801) [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 3.33% and helper 0.02% (9.99% proof) U(113,-114,1801) is Fermat and Lucas PRP! (185.740000 seconds) modified 2003-03-25 17:22:46 created 2003-01-07 18:15:32 id 64158
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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