In mathematics, Turing's method is used to verify that for any given Gram point gm there lie m + 1 zeros of ζ(s), in the region 0 < Im(s) < Im(gm), where ζ(s) is the Riemann zeta function. It was discovered by Alan Turing and published in 1953, although that proof contained errors and a correction was published in 1970 by R. Sherman Lehman. For every integer i with i < n we find a list of Gram points and a complementary list , where gi is the smallest number such that and Then the bound is achieved and we have that there are exactly m + 1 zeros of ζ(s), in the region 0 < Im(s) < Im(gm).