experimental-projects/pseudoprimes/generators/imprimitive_carmichael_better.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
            k.rad.gpf >= 3 || next
            #next if (2*5 > 40)
            var r = (2*k*p + 1)
            #r > 400 || next

            if (r.is_prime && (r.dec.gpf == p)) {
                arr << r
            }
        }

        #arr = arr.grep { _ > 10_000}

      #  var copy = arr.clone
       # arr || next

      #  for k in (2..copy.max.ilog2) {

       # arr = copy.grep{ _ > 2**k}
       # next if (arr == copy)

        var t = binomial(arr.len, m)

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

        #~ arr = arr.last(19448)

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

        #~ denominations = arr
        #~ change(m)

        arr.combinations(m, {|*a|
            with (a.prod) { |C|
                #break if (C > 325533792014488126487416882038879701391121)
                #break if (C.gpf / C.lpf > 40)
                if (C.is_carmichael) {
                    say C
                    say "# Imprimitive with p = #{p}: #{C}" if is_imprimitive(C)
                }
            }
            #break if (++count > 1e5)
        })
      #  }
    }
}

for p in (primes(11..457)) {
     say "# p = #{p}"
     generate_imprimitive(p,9)
}