Anonymous Monk,
Ok - this is an adaptation of Challenge: Nearest Palindromic Number. Since the mathematical lesson has already been explained, I decided to spruce up the Perl so that there might be a lesson in it.

#!/usr/bin/perl
use strict;
use warnings;
my $nearest_prime = nearest();
for ( map { int( rand 9998 ) + 2 } 1 .. 50 ) {
print "$_ : ", $nearest_prime->( $_ ), "\n";
}
sub nearest {
my $prime = is_prime();
return sub {
my $n = shift;
return $n if $prime->( $n );
my $pos = $n;
++$pos while ! $prime->( $pos );
$pos = $pos - $n;
my $neg = $n;
--$neg while ! $prime->( $neg );
$neg = $n - $neg;
return $pos > $neg ? $n - $neg : $n + $pos;
}
}
sub is_prime {
my %prime = map { $_ => 1 } (2, 3, 5, 7);
my %not_prime;
return sub {
my $n = shift;
return 1 if $prime{ $n };
return 0 if $n % 2 == 0 || exists $not_prime{ $n };
for ( 3 .. sqrt $n ) {
return $not_prime{ $n } = 0 if $n % $_ == 0;
}
return $prime{ $n } = 1;
};
}