How do I avoid scientific notation for large numbers?

So, I'm thinking that what you really want is just the ability to print it without scientific notation. If you're using printf, what you want is:

printf( "%f1000.0", value );
// note that 1000 is way larger than need be,
// I'm just too lazy to count the digits

With cout, try something like:

cout.setf(ios::fixed);
cout << setprecision(0) << value;

If you want to print it as a power of two (2^1000 vs 10715...), you're on your own.

There is a practical limit to how large a number that can be directly manipulated in machine registers can be. if you are using double precision floats there are a total of 64 bits, some of which are devoted to the mantissa, some to the exponent, and 1 to the sign bit.

2^1000 needs a 1001 bit integer to be represented without losing precision. In order to work with numbers like that you will need to use a library that has big number support, such as GNU MP.