2015 Number Theory: Plowing and Starring Through High Wave Forms  
Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate. To convince oneself, one has only to glance at the tables of primes which some people took the trouble to computer beyond a hundred thousand, and one perceives that there is no order and no rule. Abstract For x 0 let π(x) be the number of primes not exceeding x. The asymptotic behaviors of the
more » ... me-counting function π(x) and the n-th prime p n have been studied intensively in analytic number theory. Surprisingly, we find that π(x) and p n have many combinatorial properties which should not be ignored. In this talk we will introduce many new open problems on combinatorial properties of primes as well as some connections between primes and partition functions. We will also mention our computational evidence to support the related conjectures. / 64 Part II. Combinatorial properties of π(x) 9 / 64
doi:10.1142/9789814644938_0006 fatcat:lninta44rremhfocxhwg4cbibi