primU(7225)
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(7225) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Fibonacci primitive part |
| Proof-code(s): (*): | DK : Dubner, Keller, Cruncher |
| Decimal Digits: | 1137 (log10 is 1136.8927629599) |
| Rank (*): | 125115 (digit rank is 10) |
| Entrance Rank (*): | 8523 |
| Currently on list? (*): | no |
| Submitted: | 7/1995 |
| Last modified: | 2/4/2026 10:37:55 UTC |
| Database id: | 50812 |
| Status Flags: | none |
| Score (*): | 25.6733 (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 83
Subcategory: "Fibonacci Primitive Part"
(archival tag id 177310, 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 50812 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 7812013045...8645221001 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000305508994.txt
trial
Running N-1 test using base 23
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3777-bit number
Running N-1 test using base 29
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3777-bit number
Running N+1 test using discriminant 53, base 13+sqrt(53)
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 3777-bit number
Calling N-1 BLS with factored part 54.74% and helper 1.03% (165.31% proof)
7812013045...8645221001 is prime! (0.1500s+0.0002s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
17
19
31
41
43
47
61
67
181
541
919
1021
1361
1531
1597
1601
2161
3041
3061
3407
3469
3571
5441
7639
9521
13159
40801
53551
63443
95881
109441
852211
897601
1158551
1376321
6376021
9830081
12760031
360694291
3415914041
26030477521
72208475461
20778644396941
20862774425341
23230657239121
162716451241291
280381350009601
2843304747267841
8293976826829399
7175323114950564593
11614654211954032961
17276792316211992881
616713904085105580641
3834936832404134644974961
562627837283291940137654881
6091987724746741777931027724601
23757461609604130553429094946870847499721
15098556848842849848964622710079616350508641
29365914412631953880640421809261188743280557031914639081
320633940877modified 2026-02-04 10:37:55 created 2026-02-04 10:37:45 id 187703
field value prime_id 50812 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 23 Primality testing primU(7225) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 29 Calling Brillhart-Lehmer-Selfridge with factored part 10.22% primU(7225) is PRP! (7.260000 seconds) modified 2003-03-25 17:22:48 created 2003-01-07 04:36:05 id 63819
Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.
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