prime_openmp, a FORTRAN90 code which counts the number of primes between 1 and N, using OpenMP to carry out the calculation in parallel.
The algorithm is completely naive. For each integer I, it simply checks whether any smaller J evenly divides it. The total amount of work for a given N is thus roughly proportional to 1/2*N^2.
This program is mainly a starting point for investigations into parallelization.
Here are the counts of the number of primes for some selected values of N:
N | Pi(N), Number of Primes |
---|---|
1 | 0 |
2 | 1 |
4 | 2 |
8 | 4 |
16 | 6 |
32 | 11 |
64 | 18 |
128 | 31 |
256 | 54 |
512 | 97 |
1024 | 172 |
2048 | 309 |
4096 | 564 |
8192 | 1028 |
16384 | 1900 |
32768 | 3512 |
65536 | 6542 |
131072 | 12251 |
In the BASH shell, the program could be run with 2 threads using the commands:
export OMP_NUM_THREADS=2 ./prime_openmp
The computer code and data files described and made available on this web page are distributed under the MIT license
prime_openmp is available in a C version and a C++ version and a FORTRAN90 version.
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