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Results tagged with prime-numbers
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user 27456
Questions where prime numbers play a key-role, such as: questions on the distribution of prime numbers (twin primes, gaps between primes, Hardy–Littlewood conjectures, etc); questions on prime numbers with special properties (Wieferich prime, Wolstenholme prime, etc.). This tag is often used as a specialized tag in combination with the top-level tag nt.number-theory and (if applicable) analytic-number-theory.
0
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2
answers
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Mersenne Prime Sequences
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 …
- 5,342
4
votes
0
answers
625
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A "Take a Square Root When You Can" conjecture related to the prime factorization
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 …
- 7,500
2
votes
1
answer
2k
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Conjecture on the square root of the sum of the squares of the prime factors of a number
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:
…
CommunityBot
- 1
2
votes
1
answer
659
views
Number of primes with $-1\pmod 6$ vs. Number of primes with $+1\pmod 6$
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 …
- 103
2
votes
1
answer
351
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Conjecture on prime numbers
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 …
- 6,614
3
votes
3
answers
619
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Conjecture about a sequence of natural numbers, such that, $\forall n : A_n<P_n<A_{n+1}$
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:
$\forall n : A_n<P_n<A_{n+1}$
$ …
- 30.1k
2
votes
2
answers
289
views
What is the minimal range $[f(n),g(n)]$ that contains a prime number for every integer $n>0$?
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 …
CommunityBot
- 1
5
votes
1
answer
670
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The Nth number with M prime factors
Hi.
Suppose we arrange all natural numbers in a matrix P defined as follows:
P[I][J] = The Jth number with I prime factors. So P looks something like:
1
2 , 3 , 5 , 7 , 11 , 13 , 17 …
- 5,432