prime, an Octave 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 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.
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