Prime Chains and Pratt trees
Prime Chains and Pratt trees

Kevin Ford, University of Illinois, UrbanaChampaign
Fine Hall 214
A sequence of primes $p_1, ..., p_k$ is called a prime chain if $p_j  (p_{j+1}1)$ for each $j$; e.g. 3, 7, 29, 59. We will discuss problems about counting prime chains with certain properties, and about the existence of prime chains with various properties. The Pratt tree for a prime p is the tree with root node p and below p are the Pratt trees of the odd prime factors of $p_1$.Example: 79 ................................../\ ................................3 13 ........................................\ ........................................3 We are concerned with the normal and extremal behavior of the depth of such trees.