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prime_serial.html
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<html>
<head>
<title>
PRIME_SERIAL - Program to Count Primes
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
PRIME_SERIAL <br> Program to Count Primes
</h1>
<hr>
<p>
<b>PRIME_SERIAL</b>
is a FORTRAN90 program which
counts the number of primes between 1 and N,
and is intended as a starting point for a parallel version.
</p>
<p>
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.
</p>
<p>
Here are the counts of the number of primes for some selected values of N:
<table border="1" align="center">
<tr>
<th>N</th><th>Number of Primes</th>
</tr>
<tr>
<td>1</td><td>0</td>
</tr>
<tr>
<td>10</td><td>4</td>
</tr>
<tr>
<td>100</td><td>25</td>
</tr>
<tr>
<td>1,000</td><td>168</td>
</tr>
<tr>
<td>10,000</td><td>1,229</td>
</tr>
<tr>
<td>100,000</td><td>9,592</td>
</tr>
<tr>
<td>1,000,000</td><td>78,498</td>
</tr>
<tr>
<td>10,000,000</td><td>664,579</td>
</tr>
<tr>
<td>100,000,000</td><td>5,761,455</td>
</tr>
<tr>
<td>1,000,000,000</td><td>50,847,534</td>
</tr>
</table>
</p>
<p>
The following results were observed for the elapsed time.
<table border="1" align="center">
<tr>
<th>N</th><th>Pi</th><th>Time</th>
</tr>
<tr><td> 1</td><td> 0</td><td> 0.000030</td></tr>
<tr><td> 2</td><td> 1</td><td> 0.000016</td></tr>
<tr><td> 4</td><td> 2</td><td> 0.000016</td></tr>
<tr><td> 8</td><td> 4</td><td> 0.000017</td></tr>
<tr><td> 16</td><td> 6</td><td> 0.000020</td></tr>
<tr><td> 32</td><td> 11</td><td> 0.000030</td></tr>
<tr><td> 64</td><td> 18</td><td> 0.000057</td></tr>
<tr><td> 128</td><td> 31</td><td> 0.000147</td></tr>
<tr><td> 256</td><td> 54</td><td> 0.000452</td></tr>
<tr><td> 512</td><td> 97</td><td> 0.001548</td></tr>
<tr><td> 1024</td><td> 172</td><td> 0.005303</td></tr>
<tr><td> 2048</td><td> 309</td><td> 0.018660</td></tr>
<tr><td> 4096</td><td> 564</td><td> 0.068059</td></tr>
<tr><td> 8192</td><td> 1028</td><td> 0.246378</td></tr>
<tr><td> 16384</td><td> 1900</td><td> 0.914953</td></tr>
<tr><td> 32768</td><td> 3512</td><td> 3.380086</td></tr>
<tr><td> 65536</td><td> 6542</td><td> 12.619071</td></tr>
<tr><td> 131072</td><td> 12251</td><td> 47.412759</td></tr>
</table>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>PRIME_SERIAL</b> is available in
<a href = "../../c_src/prime_serial/prime_serial.html">a C version</a> and
<a href = "../../cpp_src/prime_serial/prime_serial.html">a C++ version</a> and
<a href = "../../f77_src/prime_serial/prime_serial.html">a FORTRAN77 version</a> and
<a href = "../../f_src/prime_serial/prime_serial.html">a FORTRAN90 version</a> and
<a href = "../../m_src/prime_serial/prime_serial.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/collatz/collatz.html">
COLLATZ</a>,
a MATLAB library which
computes and analyzes the Collatz
sequence (or "hailstone" sequence or "3n+1 sequence");
</p>
<p>
<a href = "../../f_src/fft_serial/fft_serial.html">
FFT_SERIAL</a>,
a FORTRAN90 program which
demonstrates the computation of a Fast Fourier Transform,
and is intended as a starting point for implementing a parallel version.
</p>
<p>
<a href = "../../f_src/md/md.html">
MD</a>,
a FORTRAN90 program which
carries out a molecular dynamics simulation, and is intended as
a starting point for implementing a parallel version.
</p>
<p>
<a href = "../../f_src/mxm_serial/mxm_serial.html">
MXM_SERIAL</a>,
a FORTRAN90 program which
sets up a matrix multiplication problem A=B*C,
intended as a starting point for implementing a parallel version.
</p>
<p>
<a href = "../../f_src/poisson_serial/poisson_serial.html">
POISSON_SERIAL</a>,
a FORTRAN90 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.
</p>
<p>
<a href = "../../f_src/prime_mpi/prime_mpi.html">
PRIME_MPI</a>,
a FORTRAN90 program which
counts the number of primes between 1 and N, using MPI for parallel execution.
</p>
<p>
<a href = "../../f_src/prime_openmp/prime_openmp.html">
PRIME_OPENMP</a>,
a FORTRAN90 program which
counts the number of primes between 1 and N, using OpenMP for parallel execution.
</p>
<p>
<a href = "../../f_src/quad_serial/quad_serial.html">
QUAD_SERIAL</a>,
a FORTRAN90 program which
approximates an integral using a quadrature rule,
and is intended as a starting point for parallelization exercises.
</p>
<p>
<a href = "../../f_src/quad2d_serial/quad2d_serial.html">
QUAD2D_SERIAL</a>,
a FORTRAN90 program which
approximates an integral over a 2D region using a product quadrature rule,
and is intended as a starting point for parallelization exercises.
</p>
<p>
<a href = "../../f_src/satisfy/satisfy.html">
SATISFY</a>,
a FORTRAN90 program which
demonstrates, for a particular circuit, an exhaustive search
for solutions of the circuit satisfiability problem.
</p>
<p>
<a href = "../../f_src/timer/timer.html">
TIMER</a>,
FORTRAN90 programs which
demonstrate how to compute CPU time or elapsed time.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Eratosthenes,<br>
A Method For Finding Prime Numbers,<br>
Papyrus 487, <br>
Library of Alexandria.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "prime_serial.f90">prime_serial.f90</a>, the source code.
</li>
<li>
<a href = "prime_serial.sh">prime_serial.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "prime_serial_prb.f90">prime_serial_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "prime_serial_prb.sh">prime_serial_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "prime_serial_prb_output.txt">prime_serial_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>PRIME_NUMBER</b> returns the number of primes between 1 and N.
</li>
<li>
<b>PRIME_NUMBER_SWEEP</b> does repeated timed calls to PRIME_NUMBER.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 09 November 2011.
</i>
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