local fmt = require "fmt"
local int = require "int"
require "table2"

local can_follow = {}
local arrang = {}
local bfirst = true

local function ptrs(res, n, done)
    local ad = arrang[done]
    if n - done <= 1 then
        if can_follow[ad][n] then
            if bfirst then
                fmt.tprint("%2d", arrang, #arrang)
                bfirst = false
            end
            res += 1
        end
    else
        done += 1
        for i = done, n - 1, 2 do
            local ai = arrang[i]
            if can_follow[ad][ai] then
                local aid = arrang[done]
                arrang[i], arrang[done] = aid, ai
                res = ptrs(res, n, done)
                arrang[i], arrang[done] = ai, aid
            end
        end
    end
    return res
end

local function prime_triangle(n)
    can_follow = table.create(n)
    for i = 1, n do
        can_follow[i] = table.rep(n, false)
        for j = 1, n do can_follow[i][j] = int.isprime(i + j) end
    end
    arrang = range(1, n)
    bfirst = true
    return ptrs(0, n, 1)
end

local res = {}
for i = 2, 20 do
    res:insert(prime_triangle(i))
end
print()
print(res:concat(" "))