Phi(1749, 15679)/4663253761
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(1749, 15679)/4663253761 |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | ECPP |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | c8 : Broadhurst, Water, Primo |
| Decimal Digits: | 4354 (log10 is 4353.4624054684) |
| Rank (*): | 96605 (digit rank is 3) |
| Entrance Rank (*): | 28956 |
| Currently on list? (*): | no |
| Submitted: | 5/22/2003 20:57:20 UTC |
| Last modified: | 2/4/2026 12:19:49 UTC |
| Database id: | 64778 |
| Status Flags: | Verify |
| Score (*): | 29.8588 (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.
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 644
Subcategory: "ECPP"
(archival tag id 210385, tag last modified 2026-01-31 06:37:12)
User comments about this prime (disclaimer):
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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 64778 person_id 9 machine Using: Digital Ocean Droplet what prp notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper_1100000000458210496.txt -q"Phi(1749,15679)/4663253761" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing Phi(1749,15679)/4663253761 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000000458210496.txt
trial
Running N-1 test using base 7
Generic modular reduction using generic reduction FMA3 FFT length 1536 on A 14462-bit number
Running N-1 test using base 17
Generic modular reduction using generic reduction FMA3 FFT length 1536 on A 14462-bit number
Running N-1 test using base 23
Generic modular reduction using generic reduction FMA3 FFT length 1536 on A 14462-bit number
Running N+1 test using discriminant 31, base 10+sqrt(31)
Generic modular reduction using generic reduction FMA3 FFT length 1536 on A 14462-bit number
Calling N-1 BLS with factored part 0.22% and helper 0.12% (0.79% proof)
Phi(1749,15679)/4663253761 is Fermat and Lucas PRP! (1.4477s+0.0050s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
5
11
37
53
313
601modified 2026-02-04 12:19:49 created 2026-02-04 12:19:44 id 187744
field value prime_id 64778 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 7 Primality testing Phi(1749,15679)/4663253761 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Running N-1 test using base 23 Running N+1 test using discriminant 31, base 10+sqrt(31) Calling N-1 BLS with factored part 0.22% and helper 0.12% (0.79% proof) Phi(1749,15679)/4663253761 is Fermat and Lucas PRP! (342.790000 seconds) modified 2020-07-07 22:30:47 created 2003-05-24 15:03:32 id 69646
Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
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