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

local function report_transitions(trans_map, num)
    local keys = trans_map:keys()
    keys:sort()
    fmt.print("First %s primes. Transitions prime %% 10 -> next-prime %% 10.", fmt.int(num))
    for keys as key do
        local count = trans_map[key]
        local freq = count / num * 100
        fmt.write("%d -> %d  count: %9s", key // 10, key % 10, fmt.int(count))
        fmt.print("  frequency: %4.2f%%", freq)
    end
    print()
end

-- Sieve up to the 100 millionth prime.
local sieved = int.primes(2_038_074_743, true)
local trans_map = {}
local i = 2 -- last digit of first prime (2)
local n = 2 -- index of next prime (3) in sieved
for {1e4, 1e5, 1e6, 1e7, 1e8} as num do
    while n <= num do
        local p = sieved[n]
        -- Count transition of i -> j.
        local j = p % 10
        local k = i * 10 + j
        local t = trans_map[k]
        if !t then
            trans_map[k] = 1
        else
            trans_map[k] = t + 1
        end
        i = j
        n += 1
    end
    report_transitions(trans_map, num)
end