prime, a MATLAB 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, running on a Macintosh PowerPC G5:
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 |
1,024 | 172 | 0.005303 |
2,048 | 309 | 0.018660 |
4,096 | 564 | 0.068059 |
8,192 | 1,028 | 0.246378 |
16,384 | 1,900 | 0.914953 |
32,768 | 3,512 | 3.380086 |
65,536 | 6,542 | 12.619071 |
131,072 | 12,251 | 47.412759 |
N | Pi | Time |
---|---|---|
5 | 3 | 0.000095 |
50 | 15 | 0.000123 |
500 | 95 | 0.003194 |
5000 | 669 | 0.170837 |
50,000 | 5,133 | 13.081281 |
500,000 | 41,538 | 1,076.868061 |
total = prime ( n )where
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
prime is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.
collatz, a MATLAB code which computes and analyzes the collatz sequence (or "hailstone" sequence or "3n+1 sequence");
fft_serial, a MATLAB code which demonstrates the computation of a fast fourier transform, and is intended as a starting point for implementing a parallel version.
fire_simulation, a MATLAB 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 MATLAB code which carries out a molecular dynamics simulation, and is intended as a starting point for implementing a parallel version.
mxm, a MATLAB code which sets up a matrix multiplication problem a=b*c, intended as a starting point for implementing a parallel version.
poisson, a MATLAB 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_plot a MATLAB code which displays a box plot of the prime and composite numbers.
quad, a MATLAB code which approximates an integral using a quadrature rule, and is intended as a starting point for parallelization exercises.
quad2d, a MATLAB 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 MATLAB code which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem.
search_test, a MATLAB 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.
timer_test, MATLAB codes which demonstrate how to compute cpu time or elapsed time.