If you want to find

**ALL** the primes between 507 and 10647, using only a pen and paper, then using the "Sieve of Eratosthenes" might still be the best way? To draw a 100x100 grid you'd probably need a big piece of paper

But if you want to test a

**single** given number within the above range then lookagain's method seems best to me. There are several other methods (algorithms) and if you are interested google "primality test". I don't understand how these methods work myself.

So, going back to lookagain's method, you can speed up the division process by memorising the multiples of primes that are

*just* bigger than 1000 :-

(starting at 7 because Subhotosh Khan's method is faster for 2,3, and 5)
7 -> 1001 (7 * 143)

11 -> 1001 (11 * 91)

13 -> 1001 (13 * 77)

17 -> 1003

19 -> 1007

...

then you can repeatedly subtract this from the number under test.

For example, to test if 1091 can be divided by 13, then you just test if (1091-1001) can be divided by 13. It is much easier to check if 90 can be divided by 13 ! AND you can probably see that repeated subtraction of these numbers is going to be quick.