# Tagged Questions

Use this tag if your question is about a well-known conjecture or a conjecture of your own.

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### Kolmogorov 0-1 Law Converse?

Let $(\Omega, \mathscr F, \mathbb P)$ be a probability space. Conjecture: Suppose we have events $A_1, A_2, ...$ s.t. $\forall \ A \in \bigcap_n \sigma(A_n, A_{n+1}, ...)$, $P(A) = 0$ or $1$. ...
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### Conjecture about primes and the factorial

Below $0\notin\mathbb N$. Further corrected conjecture: For all prime numbers $p>5$ there exist a prime number $q<p$ such that $q\equiv m!\!\pmod p$, $2<m<p$. or Given a prime ...
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### Is the Fermat primality test secure enough for very big numbers?

The random variable $X_m$ is the number of trials before $n\notin\mathbb P\wedge n|2^{n-1}-1$ where $n$ is an odd random integer $2^{m-1} < n < 2^m$. Computer simulations makes me believe ...
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### Legendre's Conjecture Theme (Part I)

Main Question Recently I have been thinking about the Legendre's Conjecture. I noticed that a proof of the conjecture can be obtained if we can prove any one of the following, Conjecture 1. For ...
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### Does the set of $m \in Max(ord_n(k))$ for every $n$ without primitive roots contain a pair of primes $p_1+p_2=n$?

I have made the following observation: for those n even numbers that do not have primitive roots modulo n ,$Pr(n)$, the set $M(n)$ of those $k$ having a maximum multiplicative order $ord_n(k)$ ...
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### Artin's Conjecture on Primitive Roots and the Divisors of $s(2s+1)$

Artin's conjecture on primitive roots state that given and integer $k$ that is not a perfect square or equal to $-1$ is a primitive root modulo infinitely many primes. claim: If $s$ is any ...
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### Collatz Conjecture? [closed]

I am a lover of Math, all kinds really it is a bit of a puzzle to me I'm always trying to learn something new or a new "puzzle" to try an solve for myself even though many times i just reach the same ...
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### Is always two times an even semiprime at a distance $1$ or prime to the closest previous odd semiprime?

This is an observation regarding the semiprimes, also named 2-almost primes, biprimes, or the product of two primes. This week I do not have a computer, only a tablet (hospitalized with a lot of free ...
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### Conjecture about Rabin-Miller pseudo prime test

I tested the Rabin-Miller pseudo prime algorithm using a single test value and found that the number of false calls depends on the size of the number to test, reducing to a (conjectured) negligible ...
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### Open mathematical questions for which Numerical Search promising

I am fascinated by mathematical conjectures, especially those that are believed to be false. Now I wonder, are there some mathematical conjectures for which the numerical search would be promising? ...
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### A conjecture about the prime function $p_n$

While testing my system Zet for computational mathematics I find possible relations now and then. The latest is: Conjecture: For all $(m,n)\in\mathbb Z_+^2$ except $(3,4),(4,3) \text{ and } (4,4)$...
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### conjectured generalization of euler's formula.

Given the elliptic modulus $k$ ,such that the complementary modulus is defined by $k'\equiv \sqrt{1-k^2}$,the jacobi amplitude $\phi\equiv am(u|k)$ and $K(k)$,is the complete elliptic integral of the ...
### a conjectured continued fraction for $\displaystyle\tan\left(\frac{z\pi}{4z+2n}\right)$
Given a complex number \begin{aligned}\frac{z}{n}=x+iy\end{aligned} and a gamma function $\Gamma(z)$ with $x\gt0$, it is conjectured that the following continued fraction for \$\displaystyle\tan\left(...