PRIME_OPENMP is a FORTRAN90 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:
| 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 GNU LGPL license.
PRIME_OPENMP is available in a C version and a C++ version and a FORTRAN90 version.
DIJKSTRA_OPENMP, a FORTRAN90 program which uses OpenMP to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.
FFT_OPENMP, a FORTRAN90 program which demonstrates the computation of a Fast Fourier Transform in parallel, using OpenMP.
HEATED_PLATE_OPENMP, a FORTRAN90 program which solves the steady (time independent) heat equation in a 2D rectangular region, using OpenMP to run in parallel.
HELLO_OPENMP, a FORTRAN90 program which prints out "Hello, world!" using the OpenMP parallel programming environment.
JACOBI_OPENMP, a FORTRAN90 program which illustrates the use of the OpenMP application program interface to parallelize a Jacobi iteration solving A*x=b.
MANDELBROT_OPENMP, a FORTRAN90 program which generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set, using OpenMP for parallel execution.
MD_OPENMP, a FORTRAN90 program which carries out a molecular dynamics simulation in parallel, using OpenMP.
MULTITASK_OPENMP, a FORTRAN90 program which demonstrates how to "multitask", that is, to execute several unrelated and distinct tasks simultaneously, using OpenMP for parallel execution.
MXM_OPENMP, a FORTRAN90 program which computes a dense matrix product C=A*B, using OpenMP for parallel execution.
OPENMP, FORTRAN90 programs which illustrate the use of the OpenMP application program interface for carrying out parallel computations in a shared memory environment.
OPENMP_RCC, FORTRAN90 programs which illustrate how a FORTRAN90 program, using OpenMP, can be compiled and run in batch mode on the FSU High Performance Computing (HPC) cluster operated by the Research Computing Center (RCC).
POISSON_OPENMP, a FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 program which approximates an integral using a quadrature rule, and carries out the computation in parallel using OpenMP.
RANDOM_OPENMP, a FORTRAN90 program which illustrates how a parallel program using OpenMP can generate multiple distinct streams of random numbers.
SATISFY_OPENMP, a FORTRAN90 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 FORTRAN90 program which demonstrates the default, static, and dynamic methods of "scheduling" loop iterations in OpenMP to avoid work imbalance.
SGEFA_OPENMP, a FORTRAN90 program which reimplements the SGEFA/SGESL linear algebra routines from LINPACK for use with OpenMP.
ZIGGURAT_OPENMP, a FORTRAN90 program which demonstrates how the ZIGGURAT library can be used to generate random numbers in an OpenMP parallel program.
You can go up one level to the FORTRAN90 source codes.