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Is there an approximation for the maximum difference between P(n) and n x ln(n) as a function of n, where P(n) denotes the nth prime number? In other words, given D(n) = Max(|P(n) - n x ln(n)|), is t …

Hi all. I've had this idea - a conjecture in the field of Number Theory - for a few years now. The conjecture is rather simple, as were the logical steps that I made in order to infer it, so I would …

Conjecture - no natural number $k$ exists such that: $P$ is the sequence of all primes starting from the $k$th prime $A$ is a sequence of natural numbers such that: $\forall n : A_n<P_n<A_{n+1}$ $ …

Hi. Given the following sequence (of Mersenne primes): $ A_{1} = 2 $ $ A_{n} = 2^{A_{n-1}} - 1 $ The first five elements are all prime numbers: $ 2 $ $ 2^{2}-1=3 $ $ 2^{3}-1=7 $ $ 2^{7}-1=127 …

I know the following: Proven: There is a prime number between $n$ and $2n$ for every integer $n>0$. Conjectured: There is a prime number between $n^2$ and $(n+1)^2$ for every integer $n>0$. My que …

Have not been able to get an answer to this on http://math.stackexchange.com, so trying here too... Given the following two sets: $P^-(n) = \{p \leq n : p \equiv -1\pmod 6\}$ $P^+(n) = \{p \leq n …

Given a prime $p$, let $a_n=pn+n-1$. I have noticed that $\forall{p}\exists{n}\in[2,p]:a_n\in\mathbb{P}$. For example: $p=7,a_3=23,a_4=31,a_6=47$. What is this conjecture called, and has it been pr …

Let $A_{n}$ denote the square root of the sum of the squares of the prime factors of $n$. For example, $A_{60}=\sqrt{2^2+2^2+3^2+5^2}\approx6.48$. I have recently made the following observations: …

I would tend to think that the following has already been investigated. But as implied from the title, I have no idea how to even start looking for it. Let $P_n$ denote the sum of the squares of t …