An Analytic Approximation to the Density of Twin Primes


  • Dionisel Y. Regalado
  • Rodel Azura Agusan del Sur State of Agriculture and Technology



twin primes, inter-arrival time


The highly irregular and rough fluctuations of the twin primes below or equal to a positive integer x     are considered in this study. The occurrence of a twin prime on an interval [0,x] is assumed to be random. In particular, we considered the waiting time between arrivals of twin primes as approximated by a geometric distribution which possesses the discrete memory-less property. For large n, the geometric distribution is well-approximated by the exponential distribution. The number of twin primes less or equal to x will then follow the Poisson distribution with the same rate parameter as the exponential distribution. The results are compared with the Hardy-Littlewood conjecture on the frequency of twin primes. We successfully demonstrated that for large n, the proposed model is superior to the H-L conjecture in predicting the frequency of twin primes.


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How to Cite

Regalado, D. Y., & Azura, R. (2018). An Analytic Approximation to the Density of Twin Primes. Recoletos Multidisciplinary Research Journal, 6(2).