Algorithmic and Experimental Computation of Higher-Order Safe Primes.

This paper deals with a class of special primes called safe primes. In the regular definition, an odd prime p is safe if, at least, one of (p±1)/2 is prime. Safe primes have been recommended as factors of RSA moduli. In this paper, the concept of safe primes is extended to higher-order safe primes, and an explicit formula to compute the density of this class of primes in the set of the integers is supplied. Finally, explicit conditions are provided permitting the algorithmic computation of safe primes of arbitrary order. Some experimental results are provided as well. [ABSTRACT FROM AUTHOR]