Re: [math-fun] How often does every bit matter?

Warren D Smith <warren.wds@gmail.com> wrote:

Each of the following is a prime number P, such that if any single bit of P's binary representation is changed, then you no longer have a prime. (And this is the full list of such P<10000.)

I take it that leading zeros aren't allowed. If they are, I suspect the list would be empty, as any entry would be an odd prime such that if you add any power of 2 to it the result will always be composite. I doubt such a number exists, but I can't see how to prove it.