Phi(4667, - 100)
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(4667, - 100) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Unique, ECPP |
| Proof-code(s): (*): | c47 : Chandler, Primo |
| Decimal Digits: | 8593 (log10 is 8592.0043213738) |
| Rank (*): | 84403 (digit rank is 7) |
| Entrance Rank (*): | 46057 |
| Currently on list? (*): | short |
| Submitted: | 12/26/2009 15:41:38 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 91268 |
| Status Flags: | Verify |
| Score (*): | 31.9696 (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 369
Subcategory: "ECPP"
(archival tag id 210578, tag last modified 2024-04-19 02:37:11)- Unique (archivable *)
- Prime on list: yes, rank 19
Subcategory: "Unique"
(archival tag id 210579, tag last modified 2023-05-15 15:37:15)
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 91268 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"Phi(4667,-100)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 2438507 Phi(4667,-100) has no small factor. [Elapsed time: 1.927 seconds] modified 2020-07-07 22:30:36 created 2009-12-26 15:48:01 id 111911
field value prime_id 91268 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -t -q"Phi(4667,-100)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing Phi(4667,-100) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3584,21) to FFT(3584,20) Reduced from FFT(3584,20) to FFT(3584,19) Reduced from FFT(3584,19) to FFT(3584,18) Reduced from FFT(3584,18) to FFT(3584,17) Reduced from FFT(3584,17) to FFT(3584,16) 57094 bit request FFT size=(3584,16) Running N-1 test using base 43 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3584,21) to FFT(3584,20) Reduced from FFT(3584,20) to FFT(3584,19) Reduced from FFT(3584,19) to FFT(3584,18) Reduced from FFT(3584,18) to FFT(3584,17) Reduced from FFT(3584,17) to FFT(3584,16) 57094 bit request FFT size=(3584,16) Calling Brillhart-Lehmer-Selfridge with factored part 0.28% Phi(4667,-100) is PRP! (17.9200s+0.0000s) [Elapsed time: 18.00 seconds] modified 2020-07-07 22:30:36 created 2009-12-26 15:53:02 id 111912
Query times: 0.0004 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.