e51 | Python Fiddle

class Sieve:
  def __init__(self, size):
    self.size = size
    self.sieve = {0:False, 1:False}
    i = 0
    while(i<size):
      if i in self.sieve:
        i+=1
      else:
        self.sieve[i] = True
        multiple = 2
        while(i * multiple < size):
          self.sieve[i*multiple] = False
          multiple+=1
        i+=1
  def isPrime( self, a ):
    if(a < self.size):
      return self.sieve[a]
    else:
      raise ValueError("The number is bigger than the max number in the sieve.")

def getQ(prime, mask):
  # checks if each digit of the mask is the same number,
  # if so, return it.
  while mask%10 == 0:
    mask = int(mask/10)
    prime = int(prime/10)
  testQ = prime % 10
  while(mask):
    mask = int(mask/10)
    prime = int(prime/10)
    if mask%10 == 1:
      if testQ != prime % 10:
        # Number does not match the mask
        return -1
  # Number does match the mask, and we return the digit.
  return testQ

def testPrime(prime, mask, sieve):
  # getQ finds a recurring digit q.
  # knowing this q we can add in a certain amount of the mask 
  # and see if the result is a prime number
  q = getQ(prime, mask)
  if q == -1:
    # no recurring digit match from getQ and we abort.
    return 1
  
  # initiate to one, since we already have the one we are testing from
  primesGenerated = 1
  for i in range(1,10):
    if i + q < 10:
      generatedNum = prime + i * mask
      if sieve.isPrime(generatedNum):
        primesGenerated += 1
    else:
      generatedNum = prime - (i+q+1)%10 * mask
      if sieve.isPrime(generatedNum) and generatedNum > 10**5:
        primesGenerated += 1
  return primesGenerated

def solve51():
  MySieve = Sieve(10**6)
  # 8 numbers n = [x|q][x|q]...[x|q]x.
  # Where:
  # x: static numbers, atleast 1 the last one.
  # q: numbers that change while n is still prime, either 3 or 5.
  # 
  p = []
  for x in range(10**5,10**6):
    if MySieve.isPrime(x):
      p.append(x)
  masks = ([ 
          111,1011, 1101, 1110,
          11100,11010,11001,10110,10101,10011,
          ])
  for n in p:  
    for mask in masks:
      mask *= 10
      if testPrime(n,mask,MySieve) > 7:
        print(n)
        return 0

if __name__ == '__main__':
  solve51()

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