![]() ![]() Dictionary of Statistics & Methodology: A Nontechnical Guide for the Social Sciences. Schaum’s Easy Outline of Statistics, Second Edition (Schaum’s Easy Outlines) 2nd Edition. CRC Standard Mathematical Tables, 31st ed. Furthermore, if you make that interval very short, with μ x > 0 and j under about 20, then the number of primes in the interval roughly follows a Poisson distribution (Croot, 2010). This Poisson distribution calculator uses the formula explained below to estimate the individual probability: P(x ) (e-) ( x) / x Where: x Poisson random variable. If you choose a random number that’s less than or equal to x, the probability of that number being prime is about 0.43 percent. Let’s say that that x (as in the prime counting function is a very big number, like x = 10 100. The Poisson Distribution formula is: P(x μ) = (e -μ) (μ x) / x! There is a connection between the Poisson distribution and the prime number theorem: Short intervals of primes fall into the approximate shape of a Poisson distribution.
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