Count Primes Using OpenMP

PRIME_OPENMP is a FORTRAN77 program 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:
NPi(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

The following results were observed for the elapsed time on a machine that had 2 cores:
NPi(N)Time (1 Thread)Time (2 Threads)Time (4 Threads)
16384 1900 0.377 0.293 0.220
32768 3512 1.392 1.061 0.824
65536 6542 5.221 3.883 3.012
131072 12251 19.72714.59211.672


In the BASH shell, the program could be run with 2 threads using the commands:

        export OMP_NUM_THREADS=2


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


PRIME_OPENMP is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version.

Related Data and Programs:

DIJKSTRA_OPENMP, a FORTRAN77 program which uses OpenMP to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.

FFT_OPENMP, a FORTRAN77 program which demonstrates the computation of a Fast Fourier Transform in parallel, using OpenMP.

HEATED_PLATE_OPENMP, a FORTRAN77 program which solves the steady (time independent) heat equation in a 2D rectangular region, using OpenMP to run in parallel.

HELLO_OPENMP, a FORTRAN77 program which prints out "Hello, world!" using the OpenMP parallel programming environment.

MANDELBROT_OPENMP, a FORTRAN77 program which generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set, using OpenMP for parallel execution.

MD_OPENMP, a FORTRAN77 program which carries out a molecular dynamics simulation in parallel, using OpenMP.

MULTITASK_OPENMP, a FORTRAN77 program which demonstrates how to "multitask", that is, to execute several unrelated and distinct tasks simultaneously, using OpenMP for parallel execution.

MXM_OPENMP, a FORTRAN77 program which computes a dense matrix product C=A*B, using OpenMP for parallel execution.

MXV_OPENMP, a FORTRAN77 program which compares the performance of plain vanilla Fortran and the FORTRAN90 intrinsic routine MATMUL, for the matrix multiplication problem y=A*x, with and without parallelization by OpenMP.

OPENMP, FORTRAN77 programs which illustrate the use of the OpenMP application program interface for carrying out parallel computations in a shared memory environment.

POISSON_OPENMP, a FORTRAN77 program which computes an approximate solution to the Poisson equation in a rectangle, using the Jacobi iteration to solve the linear system, and OpenMP to carry out the Jacobi iteration in parallel.

PRIME_MPI, a FORTRAN77 program which counts the number of primes between 1 and N, using MPI for parallel execution.

PRIME_PARFOR, a MATLAB program which counts the number of primes between 1 and N; it runs in parallel using MATLAB's "parfor" facility.

PRIME_SERIAL, a FORTRAN77 program which counts the number of primes between 1 and N, intended as a starting point for the creation of a parallel version.

QUAD_OPENMP, a FORTRAN77 program which approximates an integral using a quadrature rule, and carries out the computation in parallel using OpenMP.

RANDOM_OPENMP, a FORTRAN77 program which illustrates how a parallel program using OpenMP can generate multiple distinct streams of random numbers.

SATISFY_OPENMP, a FORTRAN77 program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem, using OpenMP for parallel execution.

SCHEDULE_OPENMP, a FORTRAN77 program which demonstrates the default, static, and dynamic methods of "scheduling" loop iterations in OpenMP to avoid work imbalance.

SGEFA_OPENMP, a FORTRAN77 program which reimplements the SGEFA/SGESL linear algebra routines from LINPACK for use with OpenMP.

TIMER, FORTRAN77 programs which demonstrate how to compute CPU time or elapsed time.

ZIGGURAT_OPENMP, a FORTRAN77 program which demonstrates how the ZIGGURAT library can be used to generate random numbers in an OpenMP parallel program.


  1. Eratosthenes,
    A Method For Finding Prime Numbers,
    Papyrus 487.
  2. Michael Quinn,
    Parallel Programming in C with MPI and OpenMP,
    McGraw-Hill, 2004,
    ISBN13: 978-0071232654,
    LC: QA76.73.C15.Q55.

Source Code:

Examples and Tests:

PRIME_LOCAL runs the program locally.

PRIME_ITHACA runs the program through ITHACA's batch system.

List of Routines:

You can go up one level to the FORTRAN77 source codes.

Last revised on 01 June 2010.