A prime prime primer

Formula for the nth prime using elementary arithmetical functions based in a previous formula changing the characteristic function of prime numbers.

In this paper, we propose a new primality test, and then we employ this test to find a formula for {\pi} that computes the number of primes within any interval. We finally propose a new formula that computes the nth prime number as well as the next prime for any given number

We present a constant and a recursive relation to define a sequence $f_n$ such that the floor of $f_n$ is the $n$th prime. Therefore, this constant generates the complete sequence of primes. We also show this constant is irrational and consider other sequences that can be generated using the same method.

This is an expanded account of three lectures on the distribution of prime numbers given at the Montreal NATO school on equidistribution.

A new set of formulas for primes is presented. These formulas are more efficient and grow much slower than the two known formulas of Mills and Wright. 3 new formulas are explained.

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 $\Pi_{n} =2\Pi_{n-1} - \Pi_{n-2} \pm 2 \ \ ...

In this article we gave a recurrence to obtain the n-th prime number as function of the (n-1)-th prime number.

Using inequalities of Rosser and Schoenfeld, we prove formulas for pi(n) and the n-th prime that involve only the elementary operations +,-,/ on integers, together with the floor function. Pascal Sebah has pointed out that the formula for pi(n) operates in O(n^(3/2)) time. Similar formulas were proven using Bertrand's Postulate by Stephen Regimbal, An explicit formula for the k-th prime number, Mathematics Magazine, 48 (1975), 230-23

Let $p_1, p_2, \ldots$ denote the prime numbers $2, 3, \ldots$ numbered in increasing order. The following method is used to generate primes. Start with $p_1 = 2$, $p_2 = 3$, $IpP_1 = [2, 3]$, $pP_1 =$ $\{2, 3\}$, $MIpP_1 = 3 = MpP_1$, $\pi(pP_1) = 2$ and for $j = 1, 2, \ldots$, $MIpP_{j} =$ max $IpP_{j}$, $MpP_{j} =$ max $pP_{j}$, $\pi(pP_j)$ = $\pi(IpP_j)$ = $|pP_j|$, $IpP_{j+1}$ $= [MIpP_{j}+1,$ $MpP_j^2$ $+4MpP_j+3]$ and $pP_{j+1} = \phi(IpP_{j+1}) =$ the set of all prime...

The author states an exact expression of the distribution of primes.