...and really you only have to check other primes (they're all odd numbers) after 2, which I suppose you could generate over time in an array, at least to some orders of magnitude, so that subsequent calls to said routine were further optimized...

That's what I was going to suggest. If you created an is_even function, you could rule out (on average) half of your iterations by ruling out the even numbers first. Of course that would require a special case where n=2, but that would be a single-liner.

Even as optimized as you can be, throwing it really large numbers will always take a very long time, so to give the user some kind of indication that your program is not hung, consider putting in some type of progress indicator. Since you know what the number is, you'd know about how many factors you'd have to check (is it 1 to n, or something else that's fixed?) so you could add something like this:
# Used for progress indicator
select STDERR;
$| = 1;

...


# Progress indicator, final value
$progress = ($count / $total_count) * 100;
printf "Progress: %4.1f\%\r",$progress;
# Set carriage returns back to normal after progress indicator is comp
+lete
select STDOUT;
print "\n";
$| = 0;

[download]
This works really well for a script I use that connects to several hundred servers. Of course it's only useful when you're executing it from a shell, as opposed to cron or some other background process.

Hope that helps.

In reply to Re^3: is_a_prime test? by sierpinski
in thread is_a_prime test? by Anonymous Monk

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