I solved Problem 10 of Project Euler with the following code, which works through brute force: def isPrime(n): for x in range(2, int(n**0.5)+1): if n % x == 0: return False return True def primeList(n): primes = [] for i in range(2,n): if isPrime(i): primes.append(i) return primes def sumPrimes(primelist): prime_sum = sum(primelist) return prime_sum print (sumPrimes(primeList(2000000))) The three functions work as follows: isPrime checks whether a number is a prime; primeList returns a list containing a set of prime numbers for a certain range with limit 'n', and; sumPrimes sums up the values of all numbers in a list. (This last function isn't needed, but I liked the clarity of it, especially for a beginner like me.) I then wrote a new function, primeListRec, which does exactly the same thing as primeList, to help me better understand recursion: def primeListRec(i, n): primes = [] #print i if (i != n): primes.extend(primeListRec(i+1,n)) if (isPrime(i)): primes.append(i) return primes return primes The above recursive function worked, but only for very small values, like '500'. The function caused my program to crash when I put in '1000'. And when I put in a value like '2000', Python gave me this: RuntimeError: maximum recursion depth exceeded. What did I do wrong with my recursive function? Or is there some specific way to avoid a recursion limit?