Abstract
A study of certain Hamiltonian systems has led Y. Long to conjecture the existence of innitely many primes which are not of the form p = 2bn c + 1, where 1 < < 2 is a xed irrational number. An argument of P. Ribenboim coupled with classical results about the distribution of fractional parts of irrational multiples of primes in an arithmetic progression immediately implies that this conjecture holds in a much more precise asymptotic form. Motivated by this observation, we give an asymptotic formula for the number of primes p = qbn + c + a with n N, where ; are real numbers such that is positive and irrational of nite type (which is true for almost all ) and
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