project-euler-python.py/problem 77 at master · bashareid/project-euler-python.py · GitHub

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"""It is possible to write ten as the sum of primes in exactly five different ways:

7 + 3
5 + 5
5 + 3 + 2
3 + 3 + 2 + 2
2 + 2 + 2 + 2 + 2

What is the first value which can be written as the sum of primes in over five thousand different ways?"""

def all_primes(upper_bound):
  primes = [2]
  for i in range(3, upper_bound):
    j = 0
    while j < len(primes) and primes[j] <= int(i ** 0.5):
      if i % primes[j] == 0:
        break
      j += 1
    else:
      primes.append(i)
  return primes

def is_prime(x, primes):
  sqrt = int(x ** 0.5) + 1
  for prime in primes:
    if x % prime == 0:
      return False
    if prime == primes[-1]:
      return False
    if prime > sqrt:
      return True
  return True

primes = []
primes = all_primes(100)
#print(primes)

ways = [0] * 101
ways[0] = 1
for x in primes:
    for i in range(x, 101):
        ways[i] += ways[i - x]
        if ways[i] > 5000 :
          print(i, ways[i])
          break