imprimitive_carmichael.sf

#!/usr/bin/ruby

# Generate imprimitive Carmichael numbers with n prime factors.

func is_imprimitive(n) {
    n.factor.gcd_by { .dec }**2 > lambda(n)
}

func generate_imprimitive(p, m) {

    for z in (2..100) {

        var arr = []

        for k in (1 .. 2.sqrt**z) {
            k.is_smooth(5) || next
            var r = (2*k*p + 1)
            if (r.is_prime && (r.dec.gpf == p)) {
                arr << r
            }
        }

        var t = binomial(arr.len, m)

        t >= m  || next
        t < 1e6 || break

        var count = 0
        say "# Combinations: #{t}"

        arr.combinations(m, {|*a|
            with (a.prod) { |C|
                if (C.is_carmichael) {
                    say C
                    say "# Imprimitive with p = #{p}: #{C}" if is_imprimitive(C)
                }
            }
            break if (++count > 1e5)
        })
    }
}

for p in (primes(100..457)) {
     say "# p = #{p}"
     generate_imprimitive(p,10)
}