require "bignum"
local fmt = require "fmt"

local one = bigint.one
local two = bigint.two

local function fermat(n) return (two ^ (two ^ n)) + one end

local fns = {}
print("The first 10 fermat numbers are:")
for i = 0, 9 do
    fns[i + 1] = fermat(i)
    print($"F{fmt.sub(i)} = {fns[i + 1]}")
end

print("\nFactors of the first 9 Fermat numbers:")
mpz.init()
for i = 0, 8 do
    io.write($"F{fmt.sub(i)} = ")
    local factors
    if i < 7 then
        factors = bigint.factors(fns[i + 1])
    else
        factors = mpz.factors(fns[i + 1])
    end
    fmt.lwrite(factors)
    if #factors == 1 then
        print(" (prime)")
    elseif !factors[1]:isprobableprime(10) then
        print(" (second factor is composite)")
    else
        print()
    end
end

local f = bigint.pollard(fns[10])
print($"\nThe smallest factor of F₉ is: {f}")