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by rt (16 %, 4 x 4):
A
 1, 2, 3, 4, 5, 6, 7, 8, 9
B
 1, 2, 3, 4, 5, 6, 7, 8, 9
C
 1, 2, 3, 4, 5, 6, 7, 8, 9
D
 1, 2, 3, 4, 5, 6, 7, 8, 9
E
 1, 2, 3, 4, 5, 6, 7, 8, 9

 1, 2, 3, 4, 5, 6, 7, 8, 9

 1, 2, 3, 4, 5, 6, 7, 8, 9

 1, 2, 3, 4, 5, 6, 7, 8, 9
F
 1, 2, 3, 4, 5, 6, 7, 8, 9
G
 1, 2, 3, 4, 5, 6, 7, 8, 9

 1, 2, 3, 4, 5, 6, 7, 8, 9

 1, 2, 3, 4, 5, 6, 7, 8, 9

 1, 2, 3, 4, 5, 6, 7, 8, 9
H
 1, 2, 3, 4, 5, 6, 7, 8, 9

 1, 2, 3, 4, 5, 6, 7, 8, 9

 1, 2, 3, 4, 5, 6, 7, 8, 9

4x4, interesting. (July 26, 2002)

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. I. e., 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 mentiond in the clue for B down.
G: A palindrome.