Phi(6685, - 10)
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(6685, - 10) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Unique, ECPP |
| Proof-code(s): (*): | c8 : Broadhurst, Water, Primo |
| Decimal Digits: | 4560 (log10 is 4559.9586117012) |
| Rank (*): | 96301 (digit rank is 1) |
| Entrance Rank (*): | 28211 |
| Currently on list? (*): | no |
| Submitted: | 3/31/2003 12:34:52 UTC |
| Last modified: | 2/4/2026 12:19:37 UTC |
| Database id: | 64262 |
| Status Flags: | Verify |
| Score (*): | 30.0029 (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.
- Unique (archivable *)
- Prime on list: no, rank 33
Subcategory: "Unique"
(archival tag id 210380, tag last modified 2025-08-23 01:37:16)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 626
Subcategory: "ECPP"
(archival tag id 210379, tag last modified 2026-01-31 06:37:12)
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 64262 person_id 9 machine Using: Digital Ocean Droplet what prp notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -hhelper_1100000000032354908.txt -q"Phi(6685,-10)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(6685,-10) [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000032354908.txt
Prime_Testing_Warning,
Running N-1 test using base 2
Generic modular reduction using generic reduction FMA3 FFT length 1536 on A 15148-bit number
Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 1536 on A 15148-bit number
Running N-1 test using base 7
Generic modular reduction using generic reduction FMA3 FFT length 1536 on A 15148-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 4.89%
Phi(6685,-10) is PRP! (0.7898s+0.0067s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
7
11
13
19
37
41
73
101
137
191
271
349
887
1637
9091
9901
59281
63841
99990001
1812604116731
121450506296081
909090909090909091
1111111111111111111
1289981231950849543985493631
965194617121640791456070347951751
4996731930447843676185843959746621491531100801
17
131
5882353
389045177
9999999900000001modified 2026-02-04 12:19:37 created 2026-02-04 12:19:32 id 187742
field value prime_id 64262 person_id 9 machine Linux P4 2.8GHz what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2 Primality testing Phi(6685,-10) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Calling Brillhart-Lehmer-Selfridge with factored part 1.02% Phi(6685,-10) is PRP! (13.180000 seconds) modified 2020-07-07 22:30:48 created 2003-03-31 17:59:26 id 69130
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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