Stochastic analysis of the smooth number properties and their search

The paper introduces the concept of smooth primes and their classification, depending on the properties of their simple factors, into perfectly smooth and partially smooth. It is shown that in order to search for smooth primes and their analysis, it is necessary to know how primes are distributed depending on the number of simple factors (p − 1). The problem of constructing a measure of smoothness is considered. Results are shown showing how the first 10 million numbers (p − 1) are distributed by the number of simple factors.