primU(8275)
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(8275) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Fibonacci primitive part |
| Proof-code(s): (*): | DK : Dubner, Keller, Cruncher |
| Decimal Digits: | 1380 (log10 is 1379.3219424551) |
| Rank (*): | 114473 (digit rank is 10) |
| Entrance Rank (*): | 5994 |
| Currently on list? (*): | no |
| Submitted: | 7/1995 |
| Last modified: | 2/4/2026 10:30:21 UTC |
| Database id: | 40650 |
| Status Flags: | none |
| Score (*): | 26.2774 (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 78
Subcategory: "Fibonacci Primitive Part"
(archival tag id 176791, 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 40650 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 2098661788...6512305001 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000305556828.txt
trial
Running N-1 test using base 7
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 4583-bit number
Running N-1 test using base 13
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 4583-bit number
Running N+1 test using discriminant 19, base 19+sqrt(19)
Generic modular reduction using generic reduction FMA3 FFT length 512 on A 4583-bit number
Calling N-1 BLS with factored part 50.44% and helper 0.46% (151.81% proof)
2098661788...6512305001 is prime! (0.5162s+0.0004s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
11
31
41
61
89
101
151
199
331
661
3301
9901
12301
18451
19801
39161
86461
92401
305441
474541
518101
900241
6170221
6464041
7239101
34192681
35761381
42794621
51164521
52052551
230686501
1550853481
5216440441
6202401259
15806979101
36193670561
245329617161
1595471456701
12933833823941
6982111964759801
10341247759646081
99194853094755497
1528527683761524871
13983124388817520201
16714396147923615901
345802651979922515711
472811718631231089961
845417665832830648601
964537359154707797801
6193410824599987343851
9226600585401532875481
200996663240698258054501
2848829070117112957136261
5527278404454199535821801
8239615882656632140266601
32539100603113685024545201
1456220087236423815291500998738201
86653518199165231081897196999066882785379114648231387233274688133054201
19
82657modified 2026-02-04 10:30:21 created 2026-02-04 10:30:09 id 187696
field value prime_id 40650 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(8275) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Calling Brillhart-Lehmer-Selfridge with factored part 4.78% primU(8275) is PRP! (8.050000 seconds) modified 2003-03-25 17:22:48 created 2003-01-07 05:00:14 id 63847
Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.
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