Generation and Distribution of Prime Numbers Using a Modified Lagrange Polynomial

2023/10/17 by Sivaraman, Dileep, Pillai, Branesh M., Suthakorn, Jackrit +1
#FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2401.08582

Abstract

A modified Lagrange Polynomial is introduced for polynomial extrapolation, which can be used to estimate the equally spaced values of a polynomial function. As an example of its application, this article presents a prime-generating algorithm based on a 1-degree polynomial that can generate prime numbers from consecutive primes. The algorithm is based on the condition that infinitely many prime numbers exist that satisfy the equation Π_n =2Π_n-1 - Π_n-2 ± 2 ∀ Π_n >7. where Π_n-1 and Π_n-2 are the consecutive primes.

Related

• Generating Prime Numbers -- A Fast New Method
• Prime number generation and factor elimination
• Polynomial splines interpolating prime series
• An Amazing Prime Heuristic
• The distribution of the non-prime numbers - A new Sieve