No zeros occur in this puzzle.
A: both A across and its digit sum are prime numbers.
C: both C across and its reverse are prime numbers.
E: the reverse of this prime number is a cubic number.
F: while F across equals A across multiplied with C across, the reverse of F across is a prime number.
H: A across multiplied with the digit sum of H across.
B: there are prime numbers p and q such that B down equals p^q * q^p (that is, p to the power of q multiplied with q to the power of p).
C: if you cut out the middle digit of C down, you get the same number as when you divide C down by the digit sum of B down. e.g. the first digit of C down times ten plus the last digit of C down equals C down divided by the digit sum of B down.
D: this prime number is the sum of F across and E down. Also, the first two digits of D down form a prime number, and so do the last two digits of D down.
E: E down is a multiple of both p and q, the two prime numbers mentioned in the clue for B down.
G: a palindrome.