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The Sandor-Smarandache function, denoted by SS(n), is a newly-introduced Smarandache-type arithmetic function. This paper focuses on the functions SS(30p), SS(60p), SS(210p), SS(420p) and SS(840p), where p (≥2) is a prime. At the end of the paper, four tables, giving the values of SS(30p), SS(60p), SS(210p) and SS(420p) for the first 200 primes, calculated on a computer, are given. [ABSTRACT FROM AUTHOR]

The factorial-additive optimality of primes, i.e., that the sum of prime factors is always minimum, implies that prime numbers are a solution to an integer linear programming (ILP) encoding optimization problem. The summative optimality of primes follows from Goldbach's conjecture, and is viewed as an upper efficiency limit for encoding any integer with the fewest possible additions. A consequence of the above is that primes optimally encode—multiplicatively and additively—all integers. Thus, the set P of primes is the unique, irreducible subset of ℤ—in cardinality and values—that optimally encodes all numbers in ℤ, in a factorial and summative sense. Based on these dual irreducibility/optimality properties of P, we conclude that primes are characterized by a universal "quantum type" encoding optimality that also extends to non-integers. [ABSTRACT FROM AUTHOR]