PRIME_SERIAL is a FORTRAN77 program which counts the number of primes between 1 and N, and is intended as a starting point for a parallel version.
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.
Here are the counts of the number of primes for some selected values of N:
| N | Number of Primes |
|---|---|
| 1 | 0 |
| 10 | 4 |
| 100 | 25 |
| 1,000 | 168 |
| 10,000 | 1,229 |
| 100,000 | 9,592 |
| 1,000,000 | 78,498 |
| 10,000,000 | 664,579 |
| 100,000,000 | 5,761,455 |
| 1,000,000,000 | 50,847,534 |
The following results were observed for the elapsed time.
| N | Pi | Time |
|---|---|---|
| 1 | 0 | 0.000030 |
| 2 | 1 | 0.000016 |
| 4 | 2 | 0.000016 |
| 8 | 4 | 0.000017 |
| 16 | 6 | 0.000020 |
| 32 | 11 | 0.000030 |
| 64 | 18 | 0.000057 |
| 128 | 31 | 0.000147 |
| 256 | 54 | 0.000452 |
| 512 | 97 | 0.001548 |
| 1024 | 172 | 0.005303 |
| 2048 | 309 | 0.018660 |
| 4096 | 564 | 0.068059 |
| 8192 | 1028 | 0.246378 |
| 16384 | 1900 | 0.914953 |
| 32768 | 3512 | 3.380086 |
| 65536 | 6542 | 12.619071 |
| 131072 | 12251 | 47.412759 |
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
PRIME_SERIAL is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.
COLLATZ, a MATLAB library which computes and analyzes the Collatz sequence (or "hailstone" sequence or "3n+1 sequence");
FFT_SERIAL, a FORTRAN77 program which demonstrates the computation of a Fast Fourier Transform, and is intended as a starting point for implementing a parallel version.
MD, a FORTRAN77 program which carries out a molecular dynamics simulation, and is intended as a starting point for implementing a parallel version.
MG_SERIAL, a FORTRAN77 program which a serial version of the NAS Parallel Benchmark MG (MultiGrid).
MXM_SERIAL, a FORTRAN77 program which sets up a matrix multiplication problem A=B*C, intended as a starting point for implementing a parallel version.
POISSON_SERIAL, a FORTRAN77 program which computes an approximate solution to the Poisson equation in a rectangle, and is intended as the starting point for the creation of a parallel version.
PRIME_MPI, a FORTRAN77 program which counts the number of primes between 1 and N, using MPI for parallel execution.
PRIME_OPENMP, a FORTRAN77 program which counts the number of primes between 1 and N, using OpenMP for parallel execution.
QUAD_SERIAL, a FORTRAN77 program which approximates an integral using a quadrature rule, and is intended as a starting point for parallelization exercises.
QUAD2D_SERIAL, a FORTRAN77 program which approximates an integral over a 2D region using a product quadrature rule, and is intended as a starting point for parallelization exercises.
SATISFY, a FORTRAN77 program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem.
TIMER, FORTRAN77 programs which demonstrate how to compute CPU time or elapsed time.
You can go up one level to the FORTRAN77 source codes.