1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
|
#!/usr/bin/env perl
use warnings;
use strict;
use Math::Prime::Util qw/:all/;
use List::MoreUtils qw/all/;
my $maxn = shift || 100_000_000;
prime_precalc($maxn); # Speeds up is_prime, but not necessary
my($sum, $n) = (1, 0);
forprimes {
$n = 2*$_ - 4; # 2+$n/2 is prime
if (is_prime($n+1)) { # 1+$n/1 is prime
if (moebius($n) != 0) { # n should be square free
$sum += $n if all { is_prime($_+$n/$_) } divisors($n);
}
}
} int($maxn/2);
print "$sum\n";
# This version is a little more direct.
# my($sum, $n) = (0, 0);
# forprimes {
# $n = $_-1; # 1+$n/1 is prime (hence n=1 or even)
# if (is_prime(2+($n>>1))) { # 2+$n/2 is prime (noting n is even or 1)
# if (moebius($n) != 0) { # n should be square free
# $sum += $n if all { is_prime($_+$n/$_) } divisors($n);
# }
# }
# } $maxn;
# print "$sum\n";
# We could additionally check these:
# if ( (($n+2) % 4) == 0 || $n == 1) {
# Using all is more efficient, but this works:
# $sum += $n unless scalar grep { !is_prime($_+$n/$_) } divisors($n);
|
