# Tagged Questions

For questions on prime twins.

13 views

### 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 MÃ¶bius inversion one recovers $\pi(x)$ and ...
42 views

### Primes that are neither twin, cousin or sexy [closed]

I'm reading up on prime pairs, and I had a question... I can't seem to find an answer to this anywhere, and the wikipedia list of prime types is enormous! Afraid I missed it when going through it. I ...
62 views

### Why can the sieve of eratosthenes not be used to confirm the twin primes conjecture?

I have been having fun thinking about sieves and more particularly the twin prime conjecture. As I am fairly new to this type of mathematics, I am wondering, if we use the sieve of erastothenes, aka ...
34 views

### Characterization of primes $(6n+1, 6n-1)$ that are not twins

According to OEIS Sequence A002822(https://oeis.org/A002822), it states that $6n+1$ is a twin prime $iff$ $n$ is not of the form $6ab \pm a \pm b$. I was wondering if anyone had a proof for this. ...
31 views

19 views

### for a chen prime p, what is the size of factors of p+2

Suppose the twin prime conjecture fails. Then, by Chen's theorem, there are infinitely many primes $p$ s. t. $p+2$ is a product of exactly two primes. It would be nice to know that as $p$ grows, so ...
25 views

### Factorial and primorial twin primes

Factorial primes are are primes of the form $n! \pm 1$ and primorial primes are primes of the form $p\#\pm 1$, where $p\#$ is the product of all primes $\leq p$. To cite http://www.ams.org/journals/...
208 views

### How can I calculate OEIS A144311 efficiently?

I'm looking for a way to calculate OEIS A144311 efficiently. In one sense or another, this series considers the number between "relative" twin primes. What do I mean by this? Well, the number $77$ ...
70 views

### Is this a new twin prime sieve method? Any information or comments is very appreciated.

I'm studying the twin prime numbers. Instead of sieving prime numbers, I found this method to sieve $\{x: x \neq \pm 1 \text{( mod$p$)}, x \in \mathbb{N}, p \le p_i\}$, so that $(x-1,x+1)$ will be ...
37 views

755 views

### Is there more than one occurrence of a power of two between twin primes?

$2^2$ is between the twin primes $3$ and $5$. Are there any other instances of a power of two between twin primes? If so, how many? That there are Mersenne primes (primes of the form $2^n-1$) ...
54 views

150 views

44 views

### A conditional asymptotic for $\sum_{\text{$p,p+2$twin primes}}p^{\alpha}$, when $\alpha>-1$

When I've followed a notes that show how obtain a similar asymptotic using Abel summation formula, my case with $a_n=\chi(n)$, the characteristic function taking the value 1 if $p$ is prime (in a twin ...
49 views

### Bounds on twin prime counting function

I read somewhere (unfortunately I cannot find the paper again) that the twin prime counting function $\pi_2(x)$ satisfies $\pi_2(x) \leq C\frac{x}{\log^2x}$ for some constant $C$. How would one prove (...
127 views

### Twin primes sums conjecture

I have found an interesting conjecture between twin primes sums. I don't know if it is already described by someone else. I have checked in internet, but I didn't find any mention of such conjecture. ...
21 views

### What's that work that shows there are infinitely many $2k$-prime pairs for some large enough $k$?

There was something published that said there are infinitely many pairs of primes that differ by $2k$ for some large $k$. Can you help me find it? Thanks.
83 views

70 views

### Is it known whether $6\times 10^n\pm 1$ is a twin prime for some $n>2$?

I checked the number pairs $6 \times 10^n \pm 1$ for $1 \le n \le 2000$. The only twin primes of the desired form I found are: $(59, 61)$ and $(599, 601)$. I wonder if these are the only pairs. ...
73 views

### Why doesn't this twin prime counting function work?

Quite some time ago, I made a function $f(x)$ which I thought would give me the minimum amount of prime twins equal to or lower than $x$. I have tested this function for large values of $x$ and it ...
76 views

### Is a probable prime known larger than the largest known prime?

According to Wikipedia, the largest known prime is $2^{57,885,161}-1$ with $17,425,170$ digits. Because a probable prime is usually easier to find than a proven prime (although for the Mersenne-...