文摘
Let k≥2k≥2 be a fixed natural number. We establish the existence of infinitely many pairs of consecutive primes pnpn, pn+1pn+1 satisfyingpn+1−pn≥clogpnlog2pnlog4pnlog3pn, with c being a fixed positive constant, for which the interval (pn,pn+1)(pn,pn+1) contains the k-th power of a prime number.