How to avoid numeric exception : overflow in Maple 14?

Maple 14 has isprime command which testing whether number is prime or not. It's allowed to write expressions as input data so we may write the next command :

isprime(2^(3^43-5)-1);

but I get the following error when trying to run a test :

Error, numeric exception: overflow

So my question is how to avoid this overflow error ? Should I change default stack size and if it's so how to do that on win 7 ultimate ?

Solution

Since 3^43-5 is composite, then so is 2^(3^43-5)-1. See the wikipedia page on Mersenne primes. And you can get this result quickly in Maple. So if that's all you wanted, then you're done.

> isprime( 3^43-5 );
                         false

Now, suppose that you had a prime p of comparable size to 3^43. Let's say, the very next prime higher than that.

nextprime( 3^43-5 );
                 328256967394537077679

numtheory[mersenne]( nextprime( 3^43-5 ) );
                          FAIL

Ok, so that's too unfortunate.

Try applying isprime to 2^(10^6+3)-1. (Due to normal evaluation rules of maple procedures, isprime gets the expanded argument, so has no chance to see the special form and do the cheaper test against only 10^6+3. That's what numtheory[mersenne] is for.) You'll wait a while. Now imagine how long it would take isprime to handle a number about 10^11 times as large, which is about what you'd have if you used 2^nextprime(3^43-5)-1.