Phi(427, - 1028)
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(427, - 1028) |
|---|---|
| Verification status (*): | PRP |
| Official Comment (*): | Unique, ECPP |
| Unofficial Comments: | This prime has 1 user comment below. |
| Proof-code(s): (*): | FE9 : Broadhurst, Water, Morain, FastECPP |
| Decimal Digits: | 10081 (log10 is 10080) |
| Rank (*): | 83443 (digit rank is 6) |
| Entrance Rank (*): | 41352 |
| Currently on list? (*): | yes |
| Submitted: | 5/9/2009 13:01:48 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 88149 |
| Status Flags: | Verify |
| Score (*): | 32.4648 (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 345
Subcategory: "ECPP"
(archival tag id 210440, tag last modified 2024-10-27 10:37:10)- Unique (archivable *)
- Prime on list: yes, rank 16
Subcategory: "Unique"
(archival tag id 210441, tag last modified 2023-05-15 15:37:15)
User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
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 88149 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f36{3416} -q"Phi(427,-10^28)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Factoring numbers to 36% of normal. Using modular factorization: {3416} trial factoring to 2383595230 Phi(427,-10^28) has no small factor. [Elapsed time: 1.317 seconds] modified 2020-07-07 22:30:38 created 2009-05-09 13:05:01 id 105660
field value prime_id 88149 person_id 9 machine Ditto P4 P4 what prp notes Command: /home/ditto/client/pfgw -t -q"Phi(427,-10^28)" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing Phi(427,-10^28) [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 19 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(4096,21) to FFT(4096,20) Reduced from FFT(4096,20) to FFT(4096,19) Reduced from FFT(4096,19) to FFT(4096,18) Reduced from FFT(4096,18) to FFT(4096,17) 66980 bit request FFT size=(4096,17) Running N-1 test using base 53 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(4096,21) to FFT(4096,20) Reduced from FFT(4096,20) to FFT(4096,19) Reduced from FFT(4096,19) to FFT(4096,18) Reduced from FFT(4096,18) to FFT(4096,17) 66980 bit request FFT size=(4096,17) Calling Brillhart-Lehmer-Selfridge with factored part 1.64% Phi(427,-10^28) is PRP! (23.7300s+0.0000s) [Elapsed time: 24.00 seconds] modified 2020-07-07 22:30:38 created 2009-05-09 13:08:01 id 105661
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.