Question: slow while loop

Hey all,
 I have created a nested while loop to investigate the Riemann zeta function: 

for q to 10 do
 m := 10^(-q);
  for s from 2 to 10 do
   n := 1;
   b := 1;
    while b >= m do
     b := evalf(abs(Zeta(s)-euclid(s, n)));
     n := n+1
    end do;
  print(m, s, n-1)
 end do
end do 

it prints out the least value of n suct that the difference between the zeta function and an estimate is less than some value m. The euclid procedure is a productsum already defined, using maple's inbuilt ithprime(i).

The loop works for q from 1 to about 5 and then becomes bitterly slow almost to a standstill. 

Have tried debugging and can't see the problem. (I need this to go from q from 1 to 300!!! and it barely works for q>5).

Any ideas to improve this would be most appreciated.