Phi(15, - 10125)
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: | Phi(15, - 10125) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Unique |
| Proof-code(s): (*): | C : Caldwell, Cruncher |
| Decimal Digits: | 1001 (log10 is 1000) |
| Rank (*): | 136436 (digit rank is 45) |
| Entrance Rank (*): | 26398 |
| Currently on list? (*): | no |
| Submitted: | 7/1996 |
| Last modified: | 2/4/2026 10:46:21 UTC |
| Database id: | 58840 |
| Status Flags: | none |
| Score (*): | 25.2719 (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.
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 58840 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper_1100000000013328384.txt -q"Phi(15,-10^125)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(15,-10^125) [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000013328384.txt
Prime_Testing_Warning,
Running N-1 test using base 13
Generic modular reduction using generic reduction FMA3 FFT length 320 on A 3322-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 35.32%
Phi(15,-10^125) is prime! (0.0238s+0.0051s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
11
41
43
101
173
251
271
691
751
3541
4001
5051
9091
21001
21401
25601
27961
60101
76001
162251
1610501
7019801
1797655751
10893295001
182521213001
356631541781
14103673319201
78875943472201
176144543406001
1680588011350901
42051775804956304559810859008305819975199677041099230574273451704628125001
269409792871731627664586194662281233853701011108906726055753272681082282441709251
32886082501657187247904557195788749...(92 digits)...74270656490822624175142646095920001
62092479296877182938725309701763612...(94 digits)...99902204345107547278766048583639501
95441
2021272609modified 2026-02-04 10:46:21 created 2026-02-04 10:46:16 id 187719
field value prime_id 58840 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 13 Primality testing Phi(15,-10^125) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Running N+1 test using discriminant 23, base 2+sqrt(23) Calling N-1 BLS with factored part 19.21% and helper 0.51% (58.21% proof) Phi(15,-10^125) is Fermat and Lucas PRP! (10.810000 seconds) modified 2003-03-25 17:23:05 created 2003-01-04 05:21:20 id 60355
Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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