# Tagged Questions

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

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### conjectured arithmetic properties of some continued fraction

Given the continued fraction found in this post and looking similar to the one in this post $$G(q)=\cfrac{1}{1-q+\cfrac{q(1-q)^2}{1-q^3+\cfrac{q(1-q^2)^2}{1-q^5+\cfrac{q(1-q^3)^2}{1-q^7+\ddots}}}}$$ ...
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### What's about of an analogous Riemann's function $R(X)$ for twin primes?

It is well know the so-called Riemann's explicit formula for the prime counting function $\pi(x)$ involving the density $J(x)$ for prime powers and how by Möbius inversion one recovers $\pi(x)$ and ...
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### For each prime $p>3$ there are non twin primes $q,r$ with $p^3=2q+r$

Define $\mathbb P'=\{n\in\mathbb P|n-2,n+2\notin \mathbb P\}$. Conjecture: Given a prime $p>3$, then $\exists q,r\in\mathbb P':p^3=2q+r.$ Tested for the first 10000 primes. The solutions ...
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### Conjecture: Every prime number is the difference between a prime number and a power of $2$

Conjecture: $\forall p\in\mathbb P\exists q\in\mathbb P\exists n\in \mathbb N: q-p=2^n$ Verified for the 100 first primes.
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### If $N = q^k n^2$ is an odd perfect number with Euler prime $q$, and $k=1$, does it follow that $\frac{\sigma(n^2)}{n^2} \geq 2 - \frac{5}{3q}$?

Let $\sigma=\sigma_{1}$ be the classical sum-of-divisors function. If $N = q^k n^2$ is an odd perfect number with Euler prime $q$ (i.e., $q$ satisfies $q \equiv k \equiv 1 \pmod 4$), and $k=1$, does ...
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### Does the sequence $q(n)=3n+1+\frac{1-(-1)^n}{2}$ generate all the prime numbers?

Define $$q(n)=3n+1+\frac{1-(-1)^n}{2} \quad, \quad n\in \mathbb N.$$ $$1,5,7,11,13,17,19,23,25,29,31,35,\dots$$ It seems like this formula gives all primes $>3$ (although not just primes of ...
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### Does this category have a name? (Relations as objects and relation between relations as morphisms)

Given two relations $R\subseteq A\times B$ and $R'\subseteq A'\times B'$. Is it known/used that every relation $r\subseteq R\times R'$ can be characterized by two relations $\alpha\subseteq A\times A'$...
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### Does every power of two arise as the difference of two primes?

Conjecture: For each $n\in\mathbb N$ there are primes $q<p$ with $p-q=2^n$. Verified for $n\leq 26$: ...
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### Combining a working hypothesis for odd perfect numbers with an inequality for logarithms

Euler's theorem for odd perfect numbers states that if there exists and odd perfect number, that is an odd positive integer $n$ satisfying $\sigma(n)=2n$, where $\sigma(m)=\sum_{d\mid m}d$ denotes the ...
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### Is this a known conjecture? Given odd primes $p,q$ with $p + q$ sufficiently large, must there exist a different pair $p',q'$ with $p+q = p'+q'$?

Conjecture: There is a natural number $N\in\mathbb N$ such that given odd primes $p,q$ with $p+q>N$ there are primes $p',q'$ where $p' \notin \{p,q\}$ such that $p+q=p'+q'$. Is this known?
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### Primes in the binomial transform of $[1, 1, 2, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, …]$.

This question is related to this sequence A139482. A commentator gives the following formula for $a_m$ $$a_m = {3m^2-9m+10 \above 1.5pt 2}$$ I have that you should consider the sequence $b_n =3n+2$ ...
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### For every prime $p > 3$ that is $3$ mod $4$, does $q+1 \mid p-q$ for some other prime $q$?

Yet another random conjecture about primes: Given a prime $p>3$ of the form $4n+3$. Then there exist a prime $q<p$ such that $q+1\mid p-q$. Verified for all $p<100000$.
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### Prime conjecture containing primorial: the difference between the primorial $n\#$ and the smallest prime $p > n\# + 1$ is always a prime

Help me find the exact conjecture statement. What I roughly remember is that it stated that the difference between primorial $n\#$ (product of first $n$ primes) and "some" larger number than the ...
Given complex numbers $a=x+iy$, $b=m+in$ and a gamma function $\Gamma(z)$ with $x\gt0$ and $m\gt0$, it is conjectured that the following general continued fraction which is symmetric on $a$ and $b$ is ...