The Study of density of prime numbers across equal intervals
DOI:
https://doi.org/10.70917/ijcisim-2026-3760Keywords:
Prime Numbers, Prime Density, Statistical Analysis, Chi-Square Test, R Programming, Computational Number Theory, Cryptography, Data VisualisationAbstract
Prime numbers are those numbers which are divisible by one and the number itself. Prime numbers are useful in data security and cybersecurity. In this paper all prime numbers between 2 and 100000 are considered. These numbers are divided into five equal intervals. Pairwise proportion tests were conducted over these intervals. The results for the test are as follows: Significant differences in the pairs A-D, B-E, C-E, and D-E are found. The remaining pairs A-B,A-C,B-C,C-D do not have significant differences. This concludes that the distribution of prime numbers is not uniform in the considered intervals. These outcomes confirm that the prime density is not uniform in the intervals, and the last partition has a much higher concentration of primes than the uniform distribution assumption would imply.
