The lowest solution is achieved when T is 6 and U is 24. To find the values of V to Z, just choose the lowest number for which p, p+6 and p+24 are all prime, then the next lowest without overlapping, etc. So, our V to Z are 5, 7, 17, 37 and 47.

Our A to O will then be:

A = 5

B = 7+6 = 13

C = 17+24 = 41

D = 37

E = 47+6 = 53

F = 5+24 = 29

G = 7

H = 17+6 = 23

I = 37+24 = 61

J = 47

K = 5+6 = 11

L = 7+24 = 31

M = 17

N = 37+6 = 43

O = 47+24 = 71

Giving a total of 489, using 15 of the first 20 prime numbers.

Thanks to Graham Holmes for finding this optimal solution.