2^n + 5^n is semiprime.sf

#!/usr/bin/ruby

# Numbers n such that 2^n+5^n is semiprime.
# https://oeis.org/A122116
# 3, 6, 8, 12, 14, 16, 17, 19, 28, 38, 47, 52, 64, 101, 274, 466, 1709, 2539, 5591, 6037, 8011
# a(16)-a(21) from ~~~~
# a(22) > 15213
# Cf. A082387.

# Where A082387 = { 3, 17, 19, 47, 101, 1709, 2539, 5591, 6037, 8011, 19373, 26489, 27427, ... }

for n in (15214 .. 1e6) {

    if (n.is_odd && (n < 19373)) {
        next
    }

    say "Testing: #{n}"

    if (n.is_odd) {
        is_prob_prime((2**n + 5**n)/7) || next
    }
    else {
        var N = (2**n + 5**n)
        var divs = []

        for d in (n.divisors) {

            var g = gcd(2**d + 5**d, N)

            if (g.is_between(2, N-1)) {
                say [n, g]
                divs << (g, N/g)
                divs.uniq.len > 2 && break
            }
        }

        divs = divs.uniq
        divs.len > 2 && next

        if (divs.len == 0) {
            is_semiprime(N) || next
        }
        else {
            divs.sort.all { .is_prob_prime } || next
        }
    }

    die "Found: #{n}"


    #if (is_semiprime(2**n + 5**n)) {
    #if (is_semiprime( (2**n - n + 1) * 2**n + 1)) {
     #   die "Found: #{n}"
        #print(n, ", ")
    #}
}