Across
A: X Across times 7
D: S Down + 100
G: Z Across squared
I: Z Across + 100
N: Same as H Down
P: A prime number
Q: I Across with its first digit moved to the end
R: T Across + 100
S: Same as B' Down
V: A prime number
X: First three digits of F Down
A': K Across squared
D': K Across times 21
E': Z Across times 9

Down
A: A Across + 9
B: Twice a prime number
D: A prime number
H: B' Down times 8
J: F Down times 7
L: X Across times Z Across
N: D Down times 8
O: 8 times a prime number
S: E Down times 3
U: V Across times 6
W: O Down times 3
Y: Its digits add up to 14
Z: C Down times 4
B': D Down + 1
C': M Across + 30