primU(12717)
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: | primU(12717) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Fibonacci primitive part |
| Proof-code(s): (*): | DK : Dubner, Keller, Cruncher |
| Decimal Digits: | 1761 (log10 is 1760.5118814658) |
| Rank (*): | 111750 (digit rank is 2) |
| Entrance Rank (*): | 4833 |
| Currently on list? (*): | no |
| Submitted: | 7/1995 |
| Last modified: | 2/4/2026 10:16:51 UTC |
| Database id: | 38056 |
| Status Flags: | none |
| Score (*): | 27.0393 (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.
- Fibonacci Primitive Part (archivable *)
- Prime on list: no, rank 65
Subcategory: "Fibonacci Primitive Part"
(archival tag id 176382, tag last modified 2024-10-14 00:37:17)
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 38056 person_id 9 machine Using: Digital Ocean Droplet what prime notes PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 3249985817...9106878081 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000305710435.txt
trial
Running N-1 test using base 7
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 5849-bit number
Running N-1 test using base 13
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 5849-bit number
Running N+1 test using discriminant 23, base 3+sqrt(23)
Generic modular reduction using generic reduction FMA3 FFT length 640 on A 5849-bit number
Calling N-1 BLS with factored part 85.02% and helper 1.03% (256.09% proof)
3249985817...9106878081 is prime! (0.4062s+0.0004s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
17
19
53
79
107
109
157
233
467
521
859
3079
5689
5779
10531
21529
29717
55457
90481
135721
162109
1668481
2623373
7297291
8023861
11128427
14600897
40762577
62650261
65597689
212375701
637293949
1828620361
2709524843
8036986159
12280217041
20397322999
39589685693
399660629491
1027912163389
6782976947987
8771441328469
69236563314151
92180471494753
1052645985555841
32361122672259149
7698999052751136773
7800447857397694201
39248822549379902003
461740953705414265853
17709777968841582908491
123944171348849444948627
2271388388107549761643321
7376884504680981519248993
8419838188221081942992281
14118644828958856747489895147
90164804095804073813560997011
170996733653700794564455261831
10647444606283332047355243227101
65790321679740490371744098034257
26648323522248284715048976204576561
563615729129684911988765765157388111
21104087776648187459376854003284008649
444768780203291887787553477198902918029
83446134680663989341287761437834038392531
108205581089246498532283117617925784720430322321
1502859545443710154429438583830557977854411607389
15339357080209290396745034799171857126630971274442788117
358417069436605346388200373721692702900004061867914562614681
75603148715670862787301902559019900...(208 digits)...80687928425060026776868695709282629
46931991234355955825174899287165430...(214 digits)...83016550627993641966307313601595347
17761
40933
1115842471modified 2026-02-04 10:16:51 created 2026-02-04 10:16:41 id 187687
field value prime_id 38056 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 Error opening file helper Running N-1 test using base 7 Primality testing primU(12717) [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 4.67% primU(12717) is PRP! (10.720000 seconds) modified 2003-03-25 17:22:47 created 2003-01-07 05:14:53 id 63882
Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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