A numerical semigroup is a subset S of N that contains 0, is closed under addition, and has a finite complement in N_0. The elements in N_0 minus S are called the gaps of the numerical semigroup, the largest gap is called the Frobenius number, and the number of gaps is the genus g(S) of the numerical semigroup. There have been many efforts to compute the sequence counting the number of numerical semigroups of genus g and today the sequence values are known up to n75. See https://oeis.org/A007323 for the complete list and for more information. It was conjectured in 2007 that the sequence is increasing, that each term is at least the sum of the two previous terms, and that the ratio between each term and the sum of the two previous terms approaches one as the genus grows to infinity, which is equivalent to have a growth rate approaching the golden ratio. The last statement of the conjecture was proved by Alex Zhai. We have developed a new algorithm to explore and count the numerical semigroups of a given genus which uses the unleaved version of the tree of numerical semigroups. In this project we plan to compute the number of numerical semigroups of genus larger than 70.