Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with prime-numbers
Search options answers only
not deleted
user 18060
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.
5
votes
Accepted
How to explain a particular property of the second-to-last bits of primes?
I think the phenomena you observe are explained more by the way you construct $B_0$ and $B_1$ than by the properties of primes (though properties of primes seem to play a role). If we suppose instead …
- 148k
8
votes
A set of integers whose factorial can be written as a product of two factorials
By comparing the growth of the $p$-divisibility of the factorial compared to its size, we can see that one of the numbers must be much smaller than the other.
Using Geoff's estimate at the prime $2$, …
- 148k
11
votes
Accepted
Relatively primes spirals
First note that, in the path, the coordinates are always positive, because whenever any coordinate decreases to $1$ you hit a relatively prime point, turn, hit another relatively prime point, and then …
- 148k
6
votes
Accepted
Random pseudoprimes vs. primes
The first Hardy-Littlewood conjecture holds, with a different constant term. The reason is because the constant term is determined by the many congruence conditions on primes - e.g., the fact that all …
- 148k
6
votes
Accepted
Prime factor distribution over $\mathbb{N}$
This will converge to $0$ for all $x$ except possibly $\frac{1}{d}$ for natural numbers $d$.
To check this, it suffices to show that $\delta_n(x)=0$ for all $n$ sufficiently large, for any such $x$. T …
- 148k
6
votes
Accepted
Numbers with large prime exponents and the ABC conjecture
If $a,b,c$ are $N$-power min then $\operatorname{rad}(abc) \leq (abc)^{1/N} \leq c^{ 3/N}$
and the $abc$ conjecture implies that $$c< K_\epsilon \operatorname{rad}(abc)^{1+\epsilon} \leq K_\epsilon c …
- 148k
9
votes
What is known about the prime number theorem for Beurling generalised primes
We can express the inverse zeta function $$ \prod_{i} (1 - x_i^{-s}) = \sum_ x \mu(x) x^{-s} = \int_1^{\infty} \left(\sum_{y \leq x } \mu(y) \right) s x^{-s-1} dx $$
From this integral representation …
- 148k
29
votes
Accepted
A surprising conjecture about twin primes
Suppose $n-1$ and $n+1$ are both primes.
$\gcd(an+b,bn+a)$ divides $an+b - (bn+a) = (a-b)(n-1)$.
There are two cases. If $n-1$ divides $\gcd(an+b,bn+a)$ then $b=n-1-a$ so $an+b= (n-1) (a+1)$ and $bn …
- 148k
19
votes
What is the importance of Polignac’s conjecture?
As far as I know, the twin primes conjecture doesn't have applications.
It is considered interesting because it is an extreme example of the kind of simple to state, hard to solve problems that are fa …
- 148k
4
votes
Accepted
Rational prime factors in the components of powers of Gaussian primes
We have the following generalization: Let $K$ be a quadratic extension of $\mathbb Q$, $\mathcal O_K$ the ring of integers, $q$ an odd prime of $\mathbb Q$ unramified in $K$, and $x \in \mathcal O_K$ …
- 148k
12
votes
Accepted
Prime gaps within which every "small" prime appears as a factor: Are there only finitely man...
As noted by Will Jagy in the comments, this is closely related to the size of prime gaps: Any gap of size at least $\sqrt{m}$ has this property.
In fact, every gap with this property has size at least …
- 148k
7
votes
Accepted
A new convolution, on function of $\mathbb F_p^n$ to $\mathbb F_p$ still zero?
As long as $n \geq p+1$, two of the entries of $x$ must be the same by the pigeonhole principle. Let $\tau$ be a transposition fixing those two entries. Then $s(\sigma \circ \tau) = -s(\sigma)$ but $x …
- 148k
11
votes
Number of points on a surface modulo p
For $s \geq 6$ this is elementary as one can use the Weil bound for Jacobi sums, which predates Weil. By orthogonality of characters, we can express the number of points as $$ \frac{1}{ (p-1)^2} \sum_ …
- 148k
6
votes
Accepted
On conjectures about the arithmetic function that counts the number of Sophie Germain primes
A reasonable conjecture is that
$$ \operatorname{Germain}(x) = 2 C \int_2^x \frac{dy}{\log^2 y} + O( x^{1-\delta} )$$ for some $\delta >0$. This is the Hardy-Littlewood conjecture with power-saving er …
- 148k
8
votes
Lines in image; are they significant to prime numbers if so how?
The vertical line going up comes from when $j=prime$, so $x=0$, $y=i$. The vertical line going down comes from the fact that $prime/2$ is always fairly far ($1/2$) away from an integer, so $x=0$, $y=- …
- 148k