This is a sieve for eliminating non-primes of the form k*b^n-1, typically searched by the Conjectures 'R Us (CRUS) project over at mersenneforum.org.

There is an executable available for download for Linux and Win64 (outdated), use the -h option to see the valid command line flags.

The CPU is responsible for reading in ABCD files and generating arrays of prime numbers to send to the GPU.
The GPU takes an array of prime numbers which may be prime factors of numbers of the form k*b^n-1. The GPU is also given a list of k-values and the n-min and n-max value from the ABCD file.

The core algorithm run on the GPU is the Baby Steps Giants Steps (BSGS) algorithm for solving the discrete logarithm.

This is very much a work in progress but these are some current performance numbers from CUDA enabled NVidia GPUs to which I have access.
The test file is R745.ABCD which contains 22 k-values, with n-min = 180,000 and n-max = 250,000 giving an n-range of 70,000.

CPU (1 core of i5-4440 @ 3.1Ghz, using SR2Sieve) - 6,000,000 p/sec

Latest update as of 17/05/23:
Nvidia GeForce RTX 2080 Ti (11750 GFLOPS, 11GB RAM, 5632kb L2 Cache, 250W) - 125,000,000 p/sec (with params -b 5 -m 4 -s 256 -Q 18) using the Linux executable
This appears to be GPU performance limited (CPU usage ~35%), and runs about 2-3 times quicker than srsieve2cl on the same GPU.

Nvidia A100 80GB PCIe (19500 GFLOPS, 80GB RAM HBM2, 40960kb L2 Cache, 250W) - 300,000,000 p/sec (with params -b 5 -m 5 -s 256 -Q 18) using the Linux executable
Changing the argument 's' makes the code vary between CPU and GPU bound, runs 2 times quicker than srsieve2cl on the same GPU.


Old speed info for other GPUs:
Nvidia GeForce GTX 1060 (3855 GFLOPS, 6GB RAM, 1536kb L2 cache, 120 Watts) - ~23,000,000 p/sec @90% TDP ~108W (wth params -b 7 -m 5 -s 256 -Q 18)
Nvidia MX150 (1177 GFLOPS, 2GB RAM, 512kb L2 cache, 25 Watts) - 6,500,000 p/sec (with params -b 5 -m 5)
Nvidia GeForce RTX 2070 Max-Q (5460 GFLOPS, 8GB RAM, 4096kb L2 Cache, 80 Watts) - 54,800,000 p/sec (with params -b 9 -m 4)
Nvidia GeForce RTX 2080 (8920 GFLOPS, 8GB RAM, 4096kb L2 Cache, 215W) - 80,000,000 p/sec (with params -b 7 -m 4 -s 256 -Q 18)
Nvidia GeForce RTX 2080 Ti (11750 GFLOPS, 11GB RAM, 5632kb L2 Cache, 250W) - 123,000,000 p/sec (with params -b 8 -m 4 -s 256 -Q 18)