# Questions tagged [twin-primes]

For questions on prime twins.

295 questions
Filter by
Sorted by
Tagged with
38 views

### Integer Parameterization of degree 2 equation: $(6x+5)y - x - 2 = (6w + 7)z - w + 4$

Finding a complete integer parameterization of $(6x+5)y - x - 2 = (6w + 7)z - w + 4$ has proved challenging. Can anyone lead me in the right direction? This is related to some nonprofessional research ...
1 vote
55 views

### Brun's theorem and the twin prime conjecture

According to the following extract taken from Wikipedia, almost all prime numbers are isolated given Brun's theorem. Doesn't that mean that there is only a finite number of twin prime numbers (they ...
• 37
35 views

61 views

### Number of divisors of composite number between and adjacent to twin primes

I am investigating properties of the number of divisors of composites between and adjacent to twin primes. When running some numeric calculations in Python (which are hopefully correct) I get the ...
60 views

### The series $\sum \frac{1}{p_iq_i}$ where $p_i,q_i$ are twin primes

I am interested in the series comprising the inverses of the products of twin prime pairs: $$\sum_i \frac{1}{p_iq_i}$$ where $p_i=6i-1,\ q_i=6i+1;\ (p_i,q_i) \in \mathbb P$. This series is equivalent ...
• 7,378
66 views

### For any $I = [p_{n} + 2, p_{n+1}^2 - 2]$ there exists an affine function in the first quadrant that lower bounds the twin prime average counter on $I$

Motivation Lemma. $h_n(x) = \sum\limits_{d \mid p_n\#}(-1)^{\omega(d)} \sum\limits_{r^2 = 1 \pmod d} \left\lfloor \frac{x - r}{d}\right\rfloor$ counts the number of twin prime averages in the ...
144 views

• 7,631
196 views

### Twin primes and circles.

For $n$ prime, noticed a pattern whenever a twin prime $(x,y) \in \mathbb{Z}^{+}$ is the only point satisfying the circle $x^2+y^2=n^2 + (n + 2)^2$ then $\Large \frac{x^2+y^2}{2}$ is prime. Example (...
• 1,913
91 views

• 85.1k
140 views

### A question on (trigonometric) prime counting function and twin prime counting function

Consider the following sum: $$S(t)=\sum_{n=5}^t\sin^2\left(\frac{π\Gamma(n)}{2n}\right)$$ As we can see this approximates $π(t)$ i.e. prime counting function pretty well. For details visit this paper ...
• 181