If a prime number is made up entirely of 1s (e.g., 11) then the number of its digits is prime.

1s_and_length_prime.py

# If a prime number is made up entirely of 1s (e.g., 11) 
# then the number of its digits is prime.

from sympy import isprime
import sys

# ValueError: Exceeds the limit (4300 digits) for integer string 
# conversion: value has 4301 digits; use sys.set_int_max_str_digits() 
# to increase the limit
sys.set_int_max_str_digits(10000)

def main():
    num = 1
    while len(str(num)) < 10000:
        if isprime(num):
            num_sum = sum(int(x) for x in list(str(num)))
            if isprime(num_sum):
                print(f"{num} is prime, sum og length ({len(str(num))}), 
                      {num_sum} is also prime")
        num = num * 10 + 1
    
if __name__ == "__main__":
    main()