local int = require "int"
local fmt = require "fmt"

local inc = {4, 2, 4, 2, 4, 6, 2, 6}

-- Assumes n is odd.
local function first_prime_factor(n)
    if n == 1     then return 1 end
    if n % 3 == 0 then return 3 end
    if n % 5 == 0 then return 5 end
    local k = 7
    local i = 1
    while k * k <= n do
        if n % k == 0 then
            return k
        else
            k = k + inc[i]
            i = i % 8 + 1
        end
    end
    return n
end

local blum = {}
local bc = 0
local counts = { [1] = 0, [3] = 0, [7] = 0, [9] =  0 }
local i = 1
while true do
    local p = first_prime_factor(i)
    if p % 4 == 3 then
        local q = i // p
        if q != p and q % 4 == 3 and int.isprime(q) then
            if bc < 50 then blum:insert(i) end
            counts[i % 10] += 1
            bc += 1
            if bc == 50 then
                print("First 50 Blum integers:")
                fmt.tprint("%3d ", blum, 10)
                print()
            elseif bc == 26828 or bc % 100_000 == 0 then
                fmt.print("The %9s Blum integer is: %9s", fmt.ord(bc, true), fmt.int(i))
                if bc == 400_000 then
                    print("\n% distribution of the first 400,000 Blum integers:")
                    for {1, 3, 7, 9} as j do
                        fmt.print("  %6.3f%% end in %d", counts[j] / 4000, j)
                    end
                    return
                end
            end
        end
    end
    i = (i % 5 == 3) ? i + 4 : i + 2
end