# PRIME_SERIAL Program to Count Primes

PRIME_SERIAL is a MATLAB 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:
NNumber of Primes
10
104
10025
1,000168
10,0001,229
100,0009,592
1,000,00078,498
10,000,000664,579
100,000,0005,761,455
1,000,000,00050,847,534

The following results were observed for the elapsed time, running on a Macintosh PowerPC G5:
NPiTime
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

NPiTime
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

### Usage:

total = prime ( n )
where
• n is the maximum number to check.
• total is the number of primes found between 2 and n.

### Languages:

PRIME_SERIAL is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

### Related Data and Programs:

COLLATZ, a MATLAB library which computes and analyzes the Collatz sequence (or "hailstone" sequence or "3n+1 sequence");

FFT_SERIAL, a MATLAB program which demonstrates the computation of a Fast Fourier Transform, and is intended as a starting point for implementing a parallel version.

FIRE_SERIAL, a MATLAB program 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 program which carries out a molecular dynamics simulation, and is intended as a starting point for implementing a parallel version.

MXM, a MATLAB program which sets up a matrix multiplication problem A=B*C, intended as a starting point for implementing a parallel version.

POISSON_SERIAL, a MATLAB 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_PARFOR, a MATLAB program which counts the number of primes between 1 and N; it runs in parallel using MATLAB's "parfor" facility.

PRIME_PLOT a MATLAB program which displays a box plot of the prime and composite numbers.

PRIME_SPMD, a MATLAB program which counts the number of primes between 1 and N; running in parallel using MATLAB's "SPMD" feature.

QUAD_SERIAL, a MATLAB program which approximates an integral using a quadrature rule, and is intended as a starting point for parallelization exercises.

QUAD2D_SERIAL, a MATLAB 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 MATLAB program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem.

SEARCH_SERIAL, a MATLAB program 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, MATLAB programs which demonstrate how to compute CPU time or elapsed time.

### Reference:

1. Eratosthenes,
A Method For Finding Prime Numbers,
Papyrus 487,
Library of Alexandria.

### Source Code:

You can go up one level to the MATLAB source codes.

Last revised on 09 November 2011.