Phi(5161, - 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(5161, - 100) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Unique, ECPP |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | c47 : Chandler, Primo |
| Decimal Digits: | 9505 (log10 is 9504.0043213738) |
| Rank (*): | 84081 (digit rank is 2) |
| Entrance Rank (*): | 62586 |
| Currently on list? (*): | yes |
| Submitted: | 12/14/2012 20:15:46 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 110404 |
| Status Flags: | Verify |
| Score (*): | 32.2824 (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 363
Subcategory: "ECPP"
(archival tag id 214821, tag last modified 2024-10-27 10:37:10)- Unique (archivable *)
- Prime on list: yes, rank 17
Subcategory: "Unique"
(archival tag id 214822, tag last modified 2023-05-15 15:37:15)
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 110404 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"Phi(5161,-100)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Phi(5161,-100) 1/1 mro=0 trial factoring to 2719581 Phi(5161,-100) has no small factor. [Elapsed time: 9.403 seconds] modified 2020-07-07 22:30:23 created 2012-12-14 20:18:02 id 150793
field value prime_id 110404 person_id 9 machine RedHat P4 P4 what prp notes Command: /home/caldwell/client/pfgw -t -q"Phi(5161,-100)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing Phi(5161,-100) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 31 Calling Brillhart-Lehmer-Selfridge with factored part 0.99% Phi(5161,-100) is PRP! (17.2999s+0.0009s) [Elapsed time: 17.00 seconds] modified 2020-07-07 22:30:23 created 2012-12-14 20:23:01 id 150794
Query times: 0.0002 seconds to select prime, 0.0007 seconds to seek comments.
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