Phi(461, - 576)
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(461, - 576) |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized unique |
| Proof-code(s): (*): | DB : Dubner, Brent, Cruncher |
| Decimal Digits: | 1270 (log10 is 1269.7943423747) |
| Rank (*): | 118585 (digit rank is 10) |
| Entrance Rank (*): | 14683 |
| Currently on list? (*): | no |
| Submitted: | 7/1996 |
| Last modified: | 2/4/2026 10:31:29 UTC |
| Database id: | 44438 |
| Status Flags: | none |
| Score (*): | 26.0189 (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 1581
Subcategory: "Generalized Unique"
(archival tag id 225625, 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 44438 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper_1100000000696815819.txt -q"Phi(461,-576)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(461,-576) [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000696815819.txt
Prime_Testing_Warning,
Running N-1 test using base 17
Generic modular reduction using generic reduction FMA3 FFT length 384 on A 4228-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 34.21%
Phi(461,-576) is prime! (0.0703s+0.0063s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
11
23
41
47
61
461
3911
5521
5791
41953
98809
124799
304751
331777
346201
350521
119179481
1801385941
57162680989
124281991781
2479666140481
5576648219381
58769065453824529
319450184013149177
492913612417684781
34280564819457878501
22496867303759173834520497
2489094227090357421904887101
823726680813589047661907783761
4533131025237192598063562585025900950659393
93632952077568910761256947741097303472439618798709
44731529871753099640067792599341898160322189070269334151
473176889325889360491373587423276626174063538145009837097
425987350793392015047640587379172951796351445754782369156183681
3947modified 2026-02-04 10:31:29 created 2026-02-04 10:31:24 id 187698
field value prime_id 44438 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 17 Primality testing Phi(461,-576) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 19 Running N+1 test using discriminant 31, base 12+sqrt(31) Calling N-1 BLS with factored part 3.32% and helper 0.28% (10.27% proof) Phi(461,-576) is Fermat and Lucas PRP! (17.480000 seconds) modified 2003-03-25 17:23:01 created 2003-01-04 16:51:37 id 61239
Query times: 0.0004 seconds to select prime, 0.0004 seconds to seek comments.
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