(1) Sum of the squares of the digits of a prime is another prime number
For example, 11, 1^2 + 1^2 = 2 is prime
the prime number 23, 2^2 + 3^2 = 13
the prime number 41, 4^2 + 1^2 = 17
the prime number 61, 6^2 + 1^2 = 37
the prime number 83, 8^2 + 3^2 = 73
the prime number 101, 1^2 + 0^2 + 1^2 = 2
the prime number 113, 1^2 + 1^2 + 3^2 = 11
the prime number 317
3^2 + 1^2 + 7^2 = 59 is a prime number
Sum of the cubes of the digits of a prime is another prime number
>> 821, 823, 827, 829 are primes
8^3 + 2^3 + 1^3 = 521 is prime
8^3 + 2^3 + 3^3 = 547 is prime
8^3 + 2^3 + 7^3 = 863 is prime
8^3 + 2^3 + 9^3 = 1249 is prime
Find other examples.
(2) When replacing each digit of a prime with…
(a) its square
(b) its cube
(c) (a) & (b)
results in two new primes
For example, the prime number 983
9^2 = 81, 8^2 = 64 & 3^2 = 9
9^3 = 729, 8^3 = 512 & 3^3 = 27
The new numbers, 81649 is prime & 72951227 is prime
Find other examples.
