TY - JOUR
AU - Dionisel Regalado
AU - Rodel Azura
PY - 2019/01/10
Y2 - 2019/05/20
TI - An Analytic Approximation to the Density of Twin Primes
JF - Recoletos Multidisciplinary Research Journal
JA - RMRJ
VL - 6
IS - 2
SE - Articles
DO - 10.32871/rmrj1806.02.05
UR - https://rmrj.usjr.edu.ph/index.php/RMRJ/article/view/532
AB - 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.
ER -