# Additive primes: primes whose sum of digits is also prime
def is_prime(n: int) -> bool:
"""Check if a number is prime."""
if n < 2:
return False
if n % 2 == 0:
return n == 2
if n % 3 == 0:
return n == 3
i = 5
while i * i <= n:
if n % i == 0:
return False
i += 2
if n % i == 0:
return False
i += 4
return True
def sum_digits(n: int) -> int:
"""Compute the sum of digits of a number."""
s = 0
while n > 0:
s += n % 10
n //= 10
return s
def is_additive_prime(n: int) -> bool:
"""Check if a number is an additive prime."""
return is_prime(n) and is_prime(sum_digits(n))
def main():
TOP = 500
count = 0
for n in range(1, TOP):
if is_additive_prime(n):
print(f"{n:3d}", end="")
count += 1
if count % 10 == 0:
print()
else:
print(" ", end="")
print("\n")
print(f"Total additive primes = {count}")
if __name__ == "__main__":
main()
'''
run:
2 3 5 7 11 23 29 41 43 47
61 67 83 89 101 113 131 137 139 151
157 173 179 191 193 197 199 223 227 229
241 263 269 281 283 311 313 317 331 337
353 359 373 379 397 401 409 421 443 449
461 463 467 487
Total additive primes = 54
'''
