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The frequency of occurrence of prime numbers at unit number spacing intervalsexhibits selfsimilar fractal fluctuations concomitant with inverse power lawform for power spectrum generic to dynamical systems in nature such as fluidflows, stock market fluctuations, population dynamics, etc. The physics oflong-range correlations exhibited by fractals is not yet identified. A recentlydeveloped general systems theory visualises the eddy continuum underlyingfractals to result from the growth of large eddies as the integrated mean ofenclosed small scale eddies, thereby generating a hierarchy of eddycirculations, or an inter-connected network with associated long-rangecorrelations. The model predictions are as follows: (i) The probabilitydistribution and power spectrum of fractals follow the same inverse power lawwhich is a function of the golden mean. The predicted inverse power lawdistribution is very close to the statistical normal distribution forfluctuations within two standard deviations from the mean of the distribution.(ii) Fractals signify quantumlike chaos since variance spectrum representsprobability density distribution, a characteristic of quantum systems such aselectron or photon. (ii) Fractal fluctuations of frequency distribution ofprime numbers signify spontaneous organisation of underlying continuum numberfield into the ordered pattern of the quasiperiodic Penrose tiling pattern. Themodel predictions are in agreement with the probability distributions and powerspectra for different sets of frequency of occurrence of prime numbers at unitnumber interval for successive 1000 numbers. Prime numbers in the first 10million numbers were used for the study.

Universal Characteristics of Fractal Fluctuations in Prime Number Distribution