Can every natural number be formed as the difference of two primes?

Can every natural number be formed as the difference of two primes?

No!  Most odd numbers can't, unless they happen to be 2 less than a prime number, as the difference between two prime numbers is even, unless one of them is 2.

Mmmmm....that's a variation on a theme of one of the great "open" questions in mathematics...!!!

It's known as The Goldbach Conjecture and it states that every positive even integer can be expressed as the sum of two primes (maybe in more than one way, too. For instance, 24 = 19+5 = 13+11). As yet, it's never been proved.........

As to your specific question, I'm not sure that's been proved, either......but maybe someone else on this site would have more information!!!!

A mathematician by the name of Lagrange did prove that every "natural" number could be written as a sum of four squares.........

Here's a link to Goldbach' Conjecture which you might find of interest :

http://en.wikipedia.org/wiki/Goldbach%27s_conjecture