Da solution

C.py

#!/bin/python3

import itertools
import math

PRIMES = [3,5,7,11,13]

def memoizePrimes():

    #limit = math.ceil(math.sqrt(1000000000000001))
    limit = 100

    for number in range(17,limit+1,2):

        sqrt = math.sqrt(number)
        for prime in PRIMES:
            if number % prime == 0:
                break
            if prime > sqrt:
                PRIMES.append(number)
                break

def checkComposite(number):
    for prime in PRIMES:
        if number != prime and number % prime == 0:
            return prime

def base10rep(num, base):
   total = 0

   #Least sig is at the beggining of written
   index = len(num)-1
   for pow in range(len(num)):
       total += (num[index-pow] * (base**pow))
   return total

def main():

    memoizePrimes()

    t = int(input())
    coinJams = []
    for i in range(t):

        # n = len, j = disticnt
        var = input().split(" ")
        n = int(var[0])
        j = int(var[1])

        for numCenter in itertools.product(range(2), repeat=n-2):
            canditate = [1]
            for item in numCenter:
                canditate.append(item)
            canditate.append(1)

            verifyList = []
            for base in range(2,11):
                numberInBase10 = base10rep(canditate, base)
                compositeTest = checkComposite(numberInBase10)

                if compositeTest is not None:
                    verifyList.append(compositeTest)

            if len(verifyList) == 9:
                coinJams.append("".join(str(x) for x in canditate) + " " + "".join(str(x) + " " for x in verifyList).rstrip())
                if len(coinJams) == j:
                    print("Case #1:")
                    for coin in coinJams:
                        print(coin)
                    return
main()