def digits9_for_evenor5(digit):
primes = []
for i in [1, 3, 7, 9]:
candidate = 1111111110 * digit + i
if miller_rabin(candidate):
primes.append(candidate)
return primes
def digits9_for_evenor5(digit):
primes = []
for i in [1, 3, 7, 9]:
candidate = 1111111110 * digit + i
if miller_rabin(candidate):
primes.append(candidate)
return primes
def digits9(digit):
primes = []
base = 1111111111
# as first digit
for i in range(1, 10):
candidate = (base - 10**9) * digit + i * 10**9
if miller_rabin(candidate):
primes.append(candidate)
# not as first digit
for i in range(10):
for d in range(9):
candidate = (base - 10**d) * digit + i * 10**d
if miller_rabin(candidate):
primes.append(candidate)
return primes
def digits9(digit):
primes = []
base = 1111111111
# as first digit
for i in range(1, 10):
candidate = (base - 10 ** 9) * digit + i * 10 ** 9
if miller_rabin(candidate):
primes.append(candidate)
# not as first digit
for i in range(10):
for d in range(9):
candidate = (base - 10 ** d) * digit + i * 10 ** d
if miller_rabin(candidate):
primes.append(candidate)
return primes
def digits8_for_evenor5(digit):
primes = []
# as first digit
for i in range(1, 10):
for j in [1, 3, 7, 9]:
candidate = i * 10 ** 9 + 111111110 * digit + j
if miller_rabin(candidate):
primes.append(candidate)
# not as first digit
bases = [1011111110, 1101111110, 1110111110, 1111011110,
1111101110, 1111110110, 1111111010, 1111111100]
for base in bases:
for i in range(10):
for j in [1, 3, 7, 9]:
candidate = base * digit + (1111111110 - base) * i + j
if miller_rabin(candidate):
primes.append(candidate)
return primes
def prime_proof(n):
n_in_digits = list(str(n))
# first digit cannot be 0
digit = n_in_digits[0]
for d in range(1, 10):
n_in_digits[0] = str(d)
if miller_rabin(int(''.join(n_in_digits))):
return False
n_in_digits[0] = digit
# latter digits
for i in range(1, len(n_in_digits)):
digit = n_in_digits[i]
for d in range(10):
n_in_digits[i] = str(d)
if miller_rabin(int(''.join(n_in_digits))):
return False
n_in_digits[i] = digit
return True
def prime_proof(n):
n_in_digits = list(str(n))
# first digit cannot be 0
digit = n_in_digits[0]
for d in range(1, 10):
n_in_digits[0] = str(d)
if miller_rabin(int(''.join(n_in_digits))):
return False
n_in_digits[0] = digit
# latter digits
for i in range(1, len(n_in_digits)):
digit = n_in_digits[i]
for d in range(10):
n_in_digits[i] = str(d)
if miller_rabin(int(''.join(n_in_digits))):
return False
n_in_digits[i] = digit
return True
def digits8_for_evenor5(digit):
primes = []
# as first digit
for i in range(1, 10):
for j in [1, 3, 7, 9]:
candidate = i * 10**9 + 111111110 * digit + j
if miller_rabin(candidate):
primes.append(candidate)
# not as first digit
bases = [
1011111110, 1101111110, 1110111110, 1111011110, 1111101110, 1111110110,
1111111010, 1111111100
]
for base in bases:
for i in range(10):
for j in [1, 3, 7, 9]:
candidate = base * digit + (1111111110 - base) * i + j
if miller_rabin(candidate):
primes.append(candidate)
return primes
def main():
primes = []
# 0, X00000000X
for i in range(1, 10):
for j in [1, 3, 7, 9]:
candidate = i * 10**9 + j
if miller_rabin(candidate):
primes.append(candidate)
# even digits
# 2, 8 digits
primes.extend(digits8_for_evenor5(2))
# 4, 9 digits
primes.extend(digits9_for_evenor5(4))
# 6, 9 digits
primes.extend(digits9_for_evenor5(6))
# 8, 8 digits
primes.extend(digits8_for_evenor5(8))
# odd digits
# 1, 9 digits
primes.extend(digits9(1))
# 3, 9 digits
primes.extend(digits9(3))
# 5, 9 digits
primes.extend(digits9_for_evenor5(5))
# 7, 9 digits
primes.extend(digits9(7))
# 9, 9 digits
primes.extend(digits9(9))
# print(primes)
print(sum(primes))
def main():
primes = []
# 0, X00000000X
for i in range(1, 10):
for j in [1, 3, 7, 9]:
candidate = i * 10 ** 9 + j
if miller_rabin(candidate):
primes.append(candidate)
# even digits
# 2, 8 digits
primes.extend(digits8_for_evenor5(2))
# 4, 9 digits
primes.extend(digits9_for_evenor5(4))
# 6, 9 digits
primes.extend(digits9_for_evenor5(6))
# 8, 8 digits
primes.extend(digits8_for_evenor5(8))
# odd digits
# 1, 9 digits
primes.extend(digits9(1))
# 3, 9 digits
primes.extend(digits9(3))
# 5, 9 digits
primes.extend(digits9_for_evenor5(5))
# 7, 9 digits
primes.extend(digits9(7))
# 9, 9 digits
primes.extend(digits9(9))
# print(primes)
print(sum(primes))
