GPU-accelerated programs for searching arithmetic progressions of primes (AP-L).
This repository contains three independent programs, each in its own subdirectory with its own README:
| Subdir | Program | What it searches |
|---|---|---|
minend/ |
minend_ap_2 |
AP-L of primes with smallest last term a+(L-1)*d ≤ B |
mindiff/ |
mindiff_ap |
AP-k of primes with minimal common difference d = primorial(k) |
prp_test/ |
(three iterations) | Fermat PRP test on GPU for N = a*p# + 1 |
Records found with this code (or earlier versions). For an up-to-date catalogue of AP records of any kind, see https://www.pzktupel.de/PAP/aprecords.php.
Each entry has the form (a+b*n)*P# + c for n = 0..L−1, where P# is a
primorial (19# = 9 699 690, 23# = 223 092 870).
| AP-L | Type | Formula | Time on RTX 4090 | Source |
|---|---|---|---|---|
| 21 | byproduct (mindiff) | (65374983581321010+n)*19# + 7456123 |
found mid-sweep | mindiff/ |
| 21 | byproduct (mindiff) | (38577912963884657+n)*19# + 9333691 |
found mid-sweep | mindiff/ |
| 22 | search exhausted (no AP-22) | (a+n)*19# + c for a ≤ 6.83594*10^16, any c < 19# |
~2 weeks | mindiff/ |
| 25 | proven minimal-end | (2526681+972979*n)*23# + 128097689 |
~2 days | minend/ |
| 26 | proven minimal-end | (15626261+1666981*n)*23# + 59138353 |
~3 days | minend/ |
These programs are research/experimental code. Sadly I lost track of which ones were used to produce the records above. Therefore, there is no guarantee that the current code in any of these directories builds, runs correctly, or was used to produce the records above. The git history captures iterations as they were, not a curated, validated lineage. Each program tests certain shapes of arithmetic progressions, not all numbers/forms are checked here, small searches might sometimes still need to be run.
See LICENSE.