PRIME_OPENMP
Count Primes Using OpenMP


PRIME_OPENMP, a C++ 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:
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

Usage:

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

        export OMP_NUM_THREADS=2
        ./prime_openmp
      

Licensing:

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

Languages:

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

Related Data and Programs:

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

FFT_OPENMP, a C++ code which demonstrates the computation of a Fast Fourier Transform in parallel, using OpenMP.

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

HELLO_OPENMP, a C++ code which prints out "Hello, world!" using the OpenMP parallel programming environment.

JACOBI_OPENMP, a C++ code which illustrates the use of the OpenMP application program interface to parallelize a Jacobi iteration solving A*x=b.

MD_OPENMP, a C++ code which carries out a molecular dynamics simulation in parallel, using OpenMP.

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

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

openmp_test, C++ codes which illustrate the use of the OpenMP application program interface for carrying out parallel computations in a shared memory environment.

POISSON_OPENMP, a C++ code 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 C++ code which counts the number of primes between 1 and N, using MPI for parallel execution.

prime_openmp_test

PRIME, a C++ code 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 C++ code which approximates an integral using a quadrature rule, and carries out the computation in parallel using OpenMP.

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

SATISFY_OPENMP, a C++ code which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfy problem, using OpenMP for parallel execution.

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

SGEFA_OPENMP, a C++ code which reimplements the SGEFA/SGESL linear algebra routines from LINPACK for use with OpenMP.

TIMER, C++ codes which demonstrate how to compute CPU time or elapsed time.

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

Reference:

  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:


Last revised on 01 April 2020.