Writing a Program to Generate Primes

Date: 12/5/95 at 17:21:52
From: Anonymous
Subject: prime numbers

I need a list of the first 100 prime numbers and a way of 
generating them.  I hope you will help me!

Thank you,
Bonnie Thurber

Date: 3/17/96 at 22:47:6
From: Doctor Jodi
Subject: Re: prime numbers

There is a list of first 10,000 primes at

http://www.utm.edu/research/primes/lists/small/10000.txt   

-Doctor Jodi,  The Math Forum

Date: 3/20/96 at 0:36:45
From: Doctor Patrick
Subject: Re: prime numbers

Hi--

The first 100 primes are  
 2  3  5  7  11  13  17  19  23  29  31  37  41  43  47  53  59  
61  67  71  73  79  83  89  97  101  103  107  109  113  127   131   
137  139  149  151  157  163  167  173  179  181  191  193  197 
199  211  223  227  229  233  239    241  251  257  263  269  271  
277  281  283  293  307  311 313  317  331  337  347  349  353    
359  367  373  379  383  389  397  401  409  419  421  431 433  
439  443  449  457  461  463    467  479  487  491  499  503  509  
521  523 541.  

The easiest way to generate them is to use a computer program 
which tests each number to see if it can be factored by any number 
up to and including that number's square root.  You can stop at 
the square root, since all other combinations of factors would 
include one number larger than the square root, and one smaller.  
Once you have gone through the smaller numbers it would be 
redundant to check the larger halves as well.  

Actually, you would only have to check a number by all of the 
primes up to its square root (Do you understand why?), but that 
would take more programming skill than I have at the moment.  If 
you need more detailed information, take a look at  

http://www.utm.edu/research/primes/prove/   

I'm attaching the program I used to find these 100 primes.  It's 
written in c++, but uses entirely straight c, except for the 
sqrt() function.

#include <stdio.h>
#include <math.h>

main ()
{
        int num, count, i, prime;

        num =2;
        for (count=0; count<100; num++) {  /* keep track of primes 
found, stop at 100, increase the value of the number tested */

                prime=1;   /* prime keeps track of if a number is 
found to be prime or not--1=prime 0=not prime /*

                for (i=2; i<=sqrt(num); i++)
                        if (num%i==0) prime=0;  /*test to see in 
num is prime */
                if (prime!=0) {
                        printf("%d ", num); /* print primes */
                        count++;} /* inclease count of primes 
found */
        }
}

-Doctor Patrick,  The Math Forum