  The present paper is devoted to the discussion of some important results on
large gaps between primes and the appearance of such gaps containing $k$-th
powers of primes of various types. These results are based on important
breakthrough results due to Goldston-Pintz-Yildirim and Maynard on small gaps
between primes which are discussed shortly. They are achieved by a combination
of the large gap result of K. Ford, B. Green, J. Maynard and T. Tao as well as
the matrix method of Maier.
