local fmt = require "fmt"

local primes = {3, 5}
local cutoff = 200
local bigone = 100_000
local cubans = {}
local big_cuban = ""
local c = 0
local show_each = true
local u = 0
local v = 1

for i = 1, (1 << 20) - 1 do
    local found = false
    u += 6
    v += u
    local mx = math.floor(math.sqrt(v))
    for primes as item do
        if item > mx then break end
        if v % item == 0 then
            found = true
            break
        end
    end
    if !found then
        c += 1
        if show_each then
            local z = primes:back()
            while z <= v - 2 do
                z += 2
                local fnd = false
                for primes as item do
                    if item > mx then break end
                    if z % item == 0 then
                        fnd = true
                        break
                    end
                end
                if !fnd then primes:insert(z) end
            end
            primes:insert(v)
            cubans:insert(fmt.int(v))
            if c == cutoff then show_each = false end
        end
        if c == bigone then
            big_cuban = fmt.int(v)
            break
        end
    end
end

print("The first 200 cuban primes are:-")
fmt.tprint("%10s", cubans:slice(1, 200), 10)

print($"\nThe 100,000th cuban prime is {big_cuban}")