The Prime Number Formula of Gandhi

TL;DR

This paper presents a formula attributed to Gandhi that allows for the immediate determination of the next prime number based on known primes, along with an elementary proof and discussion on prime order.

Contribution

It introduces a new prime number formula with an elementary proof and explores the ordering of primes on the number line.

Findings

The Gandhi formula accurately predicts the next prime from previous primes.

An elementary proof of the formula's correctness is provided.

Discussion on the ordering of primes enhances understanding of prime distribution.

Abstract

With the formula of Gandhi you can determine the on $p_n$ immedately subsequent prime $p_{n+1}$ from the knowledge of the primes $p_1, p_2, ... , p_n$. An elementary proof of its trueness will be detailed shown in this paper. Finally the question for the order of the primes on the number line will be discussed.