A across, C across & B down are primes
all the eight digits are different
no number starts with zero
primenumber(A across)
primenumber(A down)
primenumber(C across)
primenumber(B down)
all digits different(A across)
all digits different(C across)
all digits different(A down)
all digits different(B down)

1st digit of A across <> 2nd digit of B down
1st digit of A across <> 3rd digit of B down
1st digit of A across <> 2nd digit of C across

2nd digit of A across <> 2nd digit of B down
2nd digit of A across <> 3rd digit of B down
2nd digit of A across <> 2nd digit of A down
2nd digit of A across <> 3rd digit of A down
2nd digit of A across <> 2nd digit of C across

3rd digit of A across <> 2nd digit of A down
3rd digit of A across <> 3rd digit of A down
3rd digit of A across <> 2nd digit of C across

2nd digit of A down <> 2nd digit of B down
2nd digit of A down <> 3rd digit of B down
2nd digit of A down <> 2nd digit of C across

2nd digit of B down <> 1st digit of C across
2nd digit of B down <> 2nd digit of C across