In this paper we discuss major problems related to reliability of random number generators used for simulation studies. We propose the decimals of π as the most reliable random number generator as compared to certain real normal numbers as well as all families of pseudorandom number generators. A new property that a random number generator must have is introduced. Two applications are discussed.

We show that the random number generator of Marsaglia and Zaman produces the successive digits of a rational -adic number. (The -adic number system generalizes -adic numbers to an arbitrary integer base .) Using continued fractions, we derive an efficient prediction algorithm for this generator.

Abstract—Despite the low cost and simple structure to generate pseudo random number, truly random number still has its own place in many security systems. We have proposed a truly random number generator with scalable parameters, different requirements focused on cost or performance can be satisfied with proper voltage and working frequency and the randomness has passed the test under NIST SP 8...