Can you identify the five-digit sphenic palindrome

• where the sum of its digits is a palindromic prime,
• where of one its factors is a multi-digit palindromic prime, and
• the sum of its factors is also a palindromic prime?

Can you identify any other sphenic palindrome that has these characteristics?

A sphenic number is a positive integer and product of three distinct primes.
A palindromic number is a number that is the same when written forwards or backwards.

Suppose the required palindromic number is xyzyx. The sum of its 5 digits <= 45, i.e., is a 2 digit number. The only 2 digit palindromic prime is 11 which must be the sum of the digits.

Since xyzyx is a prime, x cannot be 0, even or 5, i.e., x is 1 or 3.

Therefore, feasible solutions are 12521, 13331, 14141, 31313, or 32123. 

A little factoring finds the only one that meets all the criteria is 32123 with digital sum 11, factors 7x13x353 of which 353 is a palindromic prime, and sum of factors 373 which is another palindromic prime.

Nice problem!