is every prime p equals another prime p' plus or minus a power of 2? p=p'+/-2^n? are there infinitely many primes not of this form?



form of primes:prime plus a power of 2?
127 and 331 are counterexamples. It was a conjecture of Polignac that every odd number can be written as a sum of an odd prime and a power of two, but many counterexamples have been found. They are called ["obstinate numbers"](http://oeis.org/A133122). Erdos has proved that there is an infinite arithmetic progression of obstinate numbers.


Edit (response to the added question): There will be infinitely many such prime counterexamples as a corollary to Erdos' theorem and Dirichlet's theorem on arithmetic progressions. See "Not always buried deep: selections of problems from analytic and combinatorial number theory" by P. Pollack.


