Towards cryptanalysis of prime numbers - Yusuf, B.K. (Institute of Electrical and Electronics Engineers Inc., 2016)
Natural numbers that defy decomposition into factors lower than themselves provide the basis for entrenching security in the public key encryption world. A variant algorithm of trial division of sieve of Eratosthenes, with its digits split into two unequal components and whose growth centered on displacement from its immediate neighbors (i.e., Polignac and Goldbach theorems) was fashioned out. As challenged by Euler's verdict on non-existence of a function that completely generates only primes, our formulation was based both upon multiple linear regression analysis hoping to find a multi-variate function, of degree at most 3, which can predict primes and comparison to Akaike Information Criterion (AIC) for model selection. About 20 billion lower primes of digits less than or equal 12 were subjected to various validation techniques (e.g., Sloane's A006988) and other heuristics for benchmarking purposes. Our results reveal certain desirable features illuminating prime patterns regardless of their chaotic camouflage. Â© 2016 IEEE.