challenge - prime numbers where sum of squared digits of prime number is also prime

[Juan14]

This program takes an integer from level 1: in the stack and returns the prime that satisfies the condition of the challenge in level 2: and the value of the sum of the digits of the prime squared in level 1:, if flag 1 is set, the prime will be the previous prime or else the next prime. The program is stored in a variable called SDIP.

«
WHILE
1 FS? { PREVPRIME } { NEXTPRIME } IFTE
{0} OVER →STR
WHILE DUP UNROT HEAD OBJ→ + SWAP TAIL DUP SIZE
REPEAT END DROP SQ ΣLIST DUP ISPRIME? NOT
REPEAT
DROP
END
»
SDIP [STO]

running the program with flag 1 cleared and 2 on level 1: we have:

2: 11
1: 2

deleting 2 from level 1: and running the program again we have:

2: 23
1: 13

To see how many of such primes are that are less than 1000, we create a little program

«
0 1000 1 SF @ SDIP will look for the previous prime
WHILE DUP 11 >
REPEAT
SDIP DROP SWAP 1 + SWAP
END DROP
»

running this program we have:

1: 53

To find the largest of such primes less than 100,000 we set flag 1 and run the program with 100000 in level 1:, we have:

2: 99971
1: 293