prime, a FORTRAN90 code 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 MIT license
prime is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
collatz, a MATLAB library which computes and analyzes the Collatz sequence (or "hailstone" sequence or "3n+1 sequence");
FFT_SERIAL, a FORTRAN90 code which demonstrates the computation of a Fast Fourier Transform, and is intended as a starting point for implementing a parallel version.
FIRE_SERIAL, a FORTRAN90 code which simulates a forest fire over a rectangular array of trees, starting at a single random location. It is intended as a starting point for the development of a parallel version.
MD, a FORTRAN90 code which carries out a molecular dynamics simulation, and is intended as a starting point for implementing a parallel version.
MXM_SERIAL, a FORTRAN90 code which sets up a matrix multiplication problem A=B*C, intended as a starting point for implementing a parallel version.
POISSON_SERIAL, a FORTRAN90 code 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 FORTRAN90 code which counts the number of primes between 1 and N, using MPI for parallel execution.
PRIME_OPENMP, a FORTRAN90 code which counts the number of primes between 1 and N, using OpenMP for parallel execution.
QUAD_SERIAL, a FORTRAN90 code which approximates an integral using a quadrature rule, and is intended as a starting point for parallelization exercises.
QUAD2D_SERIAL, a FORTRAN90 code 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 FORTRAN90 code which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem.
SEARCH_SERIAL, a FORTRAN90 code which searches the integers from A to B for a value J such that F(J) = C. this version of the program is intended as a starting point for a parallel approach.
SUBSET_SUM_SERIAL, a FORTRAN90 code which seeks solutions of the subset sum problem, in which it is desired to find a subset of a set of integers which has a given sum; this version of the program is intended as a starting point for a parallel approach.