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Prime number algorithm in C


is this is this solution to test if a number is a prime number or not:

* Is n a prime number?
* Return TRUE (1): n is a prime number
* Return FALSE (0): n is a *not* a prime number
int is_prime_number (int n)
long c;

if (n < 2) return FALSE;

for (c = 2; c < n; c++)
if ((n % c) == 0) return FALSE;
return TRUE;


Nov 13 '05
32 76467
Christopher Benson-Manica <at***@nospam.c yberspace.org> wrote:
osmium <r1********@com cast.net> spoke thus:
You could improve it a lot by avoiding the test for even numbers except 2 by
changing the increment. Also, once you have reached the square root of n,
any further testing is doomed to failure so you might as well stop there.
But if you insert the square root test in the obvious way you are depending
on the compiler to be smart enough to optimize it away. So it *could*
actually get slower. :-(

He could stop at n/2 and still cut the run time in half...

He could download this:


And be happy. :)

Paul Hsieh
Nov 13 '05 #31
James Hu wrote:

On 2003-11-27, Dave Thompson <da************ *@worldnet.att. net> wrote:
On Sat, 22 Nov 2003 00:11:22 -0600, James Hu <jx*@despammed. com>
On 2003-11-22, Dave Thompson <da************ *@worldnet.att. net> wrote:
> On Mon, 17 Nov 2003 11:46:08 -0600, James Hu <jx*@despammed. com>
> wrote:
>> ... v <= n/v ...
> ... v * v <= n ...

But this is prone to overflow.

In general yes, though not if you are running the loop upwards (as was
the previous-post case) and n is not almost UINT_MAX (which caveat
I didn't state). But you can add a check for v <= sqrt_of_uint_ma x,
which is actually a compile-time constant although it seems difficult
to portably write it so, and I bet it's still faster than divide.

I don't doubt multiplication is faster than division on most platforms.
But, I tend to first write code that I know will work first. I've been
bitten by multiplication overflow too many times, I'm afraid.

If you're using the `%' operator to check a candidate
for divisibility, there's an excellent chance that the
`/' to check for end-of-range is "free."

for (div = 3; number / div >= div; div += 2)
if (number % div == 0)

Many compilers will perform just one division to generate
both the quotient and the remainder.

Er*********@sun .com
Nov 13 '05 #32
Eric Sosman <Er*********@su n.com> writes:
If you're using the `%' operator to check a candidate
for divisibility, there's an excellent chance that the
`/' to check for end-of-range is "free."

for (div = 3; number / div >= div; div += 2)
if (number % div == 0)

Many compilers will perform just one division to generate
both the quotient and the remainder.

In case it isn't smart enough, you can encourage it by using the
standard C library div() function.
Peter Seebach on C99:
"[F]or the most part, features were added, not removed. This sounds
great until you try to carry a full-sized printout of the standard
around for a day."
Nov 13 '05 #33

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