prog.sf

#!/usr/bin/ruby

# Least number k > 0 such that the numerator of Sum_{i=1..k} 1/prime(i)^n is a prime.
# https://oeis.org/A126225

# a(11) >= 1019
# a(12) >= 273

func a(n) {
    var sum = 0

    for k in (1..1e6) {

        sum += (1 / prime(k)**n)
        var num = sum.nu
        var size = num.ilog10

        if (k < 1019) {
            next
        }

        say "[#{n}] Testing: #{k} -- #{size}"

        if (size > 5000) {
            if (num.trial_factor(1e6).len > 1) {
                say "1e6 - factor"
                next
            }

            if (num.trial_factor(1e7).len > 1) {
                say "1e7 - factor"
                next
            }

            if (num.trial_factor(1e8).len > 1) {
                say "1e8 - factor"
                next
            }
        }

        if (size > 20_000) {
            if (num.trial_factor(2e8).len > 1) {
                say "2e8 - factor"
                next
            }

            if (num.trial_factor(3e8).len > 1) {
                say "3e8 - factor"
                next
            }
        }

        say "- primality test"

        if (num.is_prob_prime) {
            die "\nFound: #{k}\n"
            #return k
        }
    }
}

var k = 11
say [k, a(k)]