prog.sf

#!/usr/bin/ruby

# Find the smallest prime factor of 2^(2^prime(n) - 1) - 1.
# https://oeis.org/A309130

# Known terms:
#   7, 127, 2147483647, 170141183460469231731687303715884105727, 47, 338193759479, 231733529, 62914441, 2351, 1399, 295257526626031, 18287, 106937, 863, 4703, 138863, 22590223644617

func trial_factor(n, k) {

    if (n.len < 50) {
        return n.factor
    }

    #n.ecm_factor
    n.trial_factor(k)
}

var n = 15
var p = prime(n)
var e = ipow(2, p)-1
var r = znorder(2, e)

for i in (1..1e6) {

    var k = (i*r + 1)
    k.is_prime || next

    say "Testing: #{k}"
    var F = trial_factor(2**k - 1, 1e8)

    for f in F {
        var t = powmod(2, e, f)

        if (t == 1) {
            say "[#{k}] Found: #{f}"
        }
    }
}