# What is the biggest positive integer within 100 that can be/can not be written as the differences between two positive primes?

What is the biggest positive integer within 100 that can be/can not be written as the differences between two positive primes?

Can someone answer the cannot part?

There are two parts in the question.

Differences of primes are generally even (except when $2$ is involved).
$99$ can be written as $101 - 2$. Therefore a lower bound for the largest number which cannot be written as a difference of primes is $97$. It remains to check that $100$ and $98$ actually can be written as a difference of primes. Some simple trial and error will reveal that $$101 - 3 = 98$$ $$103 - 3 = 100$$
That's where $97$ comes in. – EuYu Oct 16 '12 at 21:44