Randomness at large numbers: Experimental proof in coin toss and prime number

摘要

Randomness is a central concept to statistics and physics. Here, we conduct experimental investigations with a coin toss and prime number to show experimental evidence that tossing coins and finding last digits of prime numbers are statistically identical with respect to equally likely outcomes. The range of frequency of an outcome ( R ) is normalized by the total number of repetitions ( N ) to be the range of relative frequency ( R / N ). We find that R / N has a power-law scaling R / N ～ N sup?0.6/sup, which is valid for large numbers in both cases of a coin toss and the last digit of a prime number. This analysis, indicating R / N → 0 at N → ∞, confirms that randomness and equally likely outcomes can be valid for large numbers.