Prime divisors of shifted primes

We say that an integer is smooth if it does not have any
large prime factors.  An asymptotic formula for the smooth numbers is
known.  We will consider the same question for shifted prime numbers.
We will discuss the difficulties in proving that the above asymptotic
formula holds for shifted primes.  We will also discuss formulae for
the number of shifted primes with at least one or two large prime divisors.