Phi(59, 259)
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(59, 259) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized unique |
| Proof-code(s): (*): | c5 : Carmody, Primo |
| Decimal Digits: | 1031 (log10 is 1030.1246451621) |
| Rank (*): | 130632 (digit rank is 47) |
| Entrance Rank (*): | 49088 |
| Currently on list? (*): | no |
| Submitted: | 3/6/2001 17:27:56 UTC |
| Last modified: | 2/4/2026 10:44:30 UTC |
| Database id: | 55952 |
| Status Flags: | none |
| Score (*): | 25.3648 (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 Unique (archivable *)
- Prime on list: no, rank 1585
Subcategory: "Generalized Unique"
(archival tag id 225629, tag last modified 2026-01-09 22:37:30)
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 55952 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper_1100000000016651543.txt -q"Phi(59,2^59)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(59,2^59) [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000016651543.txt
Prime_Testing_Warning,
Running N-1 test using base 5
Generic modular reduction using generic reduction FMA3 FFT length 320 on A 3423-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 39.33%
Phi(59,2^59) is prime! (0.0169s+0.0052s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
59
233
1103
2089
2833
37171
3033169
18355609
151947067
1824726041
158799763040174619172897215593
206769486791163145000083489247
192500519847846457015380059100735911
21024547392270399617328363041287439539
20366414585170116631146147960769954...(406 digits)...14110538134298582579217628693471449
23
103
232578641434571modified 2026-02-04 10:44:30 created 2026-02-04 10:44:25 id 187716
field value prime_id 55952 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 5 Primality testing Phi(59,2^59) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 13, base 6+sqrt(13) Calling N-1 BLS with factored part 3.74% and helper 0.35% (11.57% proof) Phi(59,2^59) is Fermat and Lucas PRP! (8.620000 seconds) modified 2003-03-25 17:23:05 created 2003-01-04 05:27:14 id 60466
Query times: 0.0004 seconds to select prime, 0.0009 seconds to seek comments.
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