No zeros occur in this puzzle.

**Across**:

**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.

**Down**:

**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.