def eight_prime_family(prime,rd):
c=0
for digit in '0123456789':
n=int(prime.replace(rd,digit))
if (n>100000 and intx(n).isPrime()):
c=c+1
return c==8
def eight_prime_family(prime, rd):
c = 0
for digit in '0123456789':
n = int(prime.replace(rd, digit))
if (n > 100000 and intx(n).isPrime()):
c = c + 1
return c == 8
def problem_51():
for prime in intx(1000000).sievePrime():
if prime>100000:
s=str(prime)
last_digit=s[5:6]
if (s.count('0')==3 and eight_prime_family(s,'0') or \
s.count('1')==3 and last_digit!='1' and eight_prime_family(s,'1') or \
s.count('2')==3 and eight_prime_family(s,'2')):return s
def problem_51():
for prime in intx(1000000).sievePrime():
if prime > 100000:
s = str(prime)
last_digit = s[5:6]
if (s.count('0')==3 and eight_prime_family(s,'0') or \
s.count('1')==3 and last_digit!='1' and eight_prime_family(s,'1') or \
s.count('2')==3 and eight_prime_family(s,'2')):
return s