Project Euler 50

problem

Prime number 41 can be expressed as the sum of six consecutive prime numbers:

41 = 2 + 3 + 5 + 7 + 11 + 13.

This is the longest when a prime number less than 100 is represented by the sum of consecutive prime numbers.

Similarly, when the sum of consecutive prime numbers represents a prime number less than 1000, the longest is 953, which has 21 terms.

Which prime number is the longest when expressing a prime number less than 1 million as the sum of consecutive prime numbers?

Answer

I solved it as follows.

  1. Create a list of prime numbers pri ['list']
  2. Determine the prime number pri ['list'] [i] of a certain starting point.
  3. Create the sum s after the prime number of the starting point in the range of the maximum value MAX or less. At this time, the number of consecutive prime numbers is counted as c.
  4. If s is a prime number and c is greater than c_max, let s be ans and c_max be c.
  5. Repeat steps 2 and 4 and output the finally obtained ans.
import mymath

def main():
  MAX = 10**6
  pri = mymath.get_primes(MAX)
  pri_length = len(pri['list'])
  i, c_max, ans = 0, 0, 0
  while i < pri_length:
    s, j, c = pri['list'][i], i + 1, 1
    while j < pri_length and s + pri['list'][j]< MAX:
      s += pri['list'][j]
      c += 1
      if pri['bool'][s] and c_max < c:
        ans, c_max = s, c
      j += 1
    i += 1
  print ans
  
main()

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