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The important word in my assertion isn't mathematical, it's predict. You cannot determine the closest prime p to any number n without a primality test. Now, brute force algorithms are mathematically describable; I'm not saying they're not.

Let me give you another example. Can you tell me the closest power of 2 to a given number N? Now, can you do it without breaking down a number into its composite primes? I can, by generating the sequence of powers of 2 and looking at them. That's predictive.

Here's pseudocode for both algorithms, so you can see the difference.

```Brute-force algorithm:

sub is_power {
# Some algorithm to determine if a number is a power of two.
}

sub closest_power_of_two_brute {
my \$m = my \$n = shift;

return \$n if is_power( \$n, 2 );

while (1) {
return \$n if is_power( \$++n, 2 );
return \$m if is_power( \$--m, 2 );
}
}
```Predictive algorithm:

sub iterate_over {
my \$v = shift;
return sub {
\$v *= \$v;
};
}

sub closest_power_of_two_predictive {
my \$n = shift;

my \$it = iterate_over( 2 );

my \$l = \$it->();
while ( my \$v = \$it->() ) {
last if \$v > \$n;
\$l = \$v;
}

abs( \$n - \$l ) > abs( \$n - \$v ) ? \$v : \$l;
}

Limbic~Region's example is much better than mine.

Being right, does not endow the right to be rude; politeness costs nothing.
Being unknowing, is not the same as being stupid.
Expressing a contrary opinion, whether to the individual or the group, is more often a sign of deeper thought than of cantankerous belligerence.
Do not mistake your goals as the only goals; your opinion as the only opinion; your confidence as correctness. Saying you know better is not the same as explaining you know better.

In reply to Re^7: a close prime number by dragonchild
in thread a close prime number by Anonymous Monk

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