Question

Every twin prime average $x \gt 6$ is the sum of two twin prime averages (Code checked up to $x \leq 1,000,000$).

score 143 · Answer 1 · 2023-02-23 02:03:36

143

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Every twin prime average $x \gt 6$ is the sum of two twin prime averages (Code checked up to $x \leq 1,000,000$).

Published on 23 Feb 2023 - 2:03

score 64 · Answer 2 · 2023-04-21 06:11:55

64

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 $I$

Published on 21 Apr 2023 - 6:11

score 55 · Answer 3 · 2023-04-30 21:36:53

55

Views

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

Published on 30 Apr 2023 - 21:36

score 59 · Answer 4 · 2023-05-19 09:09:22

59

Views

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

Published on 19 May 2023 - 9:09

score 62 · Answer 5 · 2023-06-04 07:08:28

62

Views

Conjecture: It is not true that $2$ eventually always divides $f(x) = \sum_{d \mid p_{\sqrt{x+1}}\#} (d \mid x^2 - 1)$.

Published on 04 Jun 2023 - 7:08

score 61 · Answer 6 · 2023-06-11 09:29:00

61

Views

Describing the probability that n is of the form $K^2+1$ , and it is a prime number.

Published on 11 Jun 2023 - 9:29

score 66 · Answer 7 · 2023-06-23 15:16:14

66

Views

Is some twin prime average the sum of two twin prime averages, two ways?

Published on 23 Jun 2023 - 15:16

score 63 · Answer 8 · 2023-06-28 12:41:53

63

Views

primes of the form 2+pq

Published on 28 Jun 2023 - 12:41

score 176 · Answer 9 · 2023-08-16 22:09:05

176

Views

Can the sum of squares of odd primes equal the square of an odd prime?

Published on 16 Aug 2023 - 22:09

score 41 · Answer 10 · 2023-09-01 13:14:50

41

Views

A corollary of Brun's pure sieve from Opera de Cribro by Friedlander and Iwaniec

Published on 01 Sep 2023 - 13:14

score 73 · Answer 11 · 2023-09-09 07:14:33

73

Views

Can we write down a formula for the simultaneous images of the $C_q$?

Published on 09 Sep 2023 - 7:14

score 150 · Answer 12 · 2023-09-14 20:09:11

150

Views

Potential progress concerning the twin prime conjecture

Published on 14 Sep 2023 - 20:09

score 256 · Answer 13 · 2023-09-30 19:07:54

256

Views

New method to generate twin primes.

Published on 30 Sep 2023 - 19:07

score 66 · Answer 14 · 2023-10-08 04:45:25

66

Views

$A(x) = \prod_{p,q \in \Bbb{P}} (1 - \frac{x^2 - 1}{pq}) = 0$ if and only if $x$ is a twin prime average?

Published on 08 Oct 2023 - 4:45

score 476 · Answer 15 · 2023-10-18 11:47:29

476

Views

$n+1$ and $n \phi (n) + 1$ are both perfect squares if and only if $n$ is a product of twin primes?

Published on 18 Oct 2023 - 11:47

List Question

Every twin prime average $x \gt 6$ is the sum of two twin prime averages (Code checked up to $x \leq 1,000,000$).

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 $I$

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

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

Conjecture: It is not true that $2$ eventually always divides $f(x) = \sum_{d \mid p_{\sqrt{x+1}}\#} (d \mid x^2 - 1)$.

Describing the probability that n is of the form $K^2+1$ , and it is a prime number.

Is some twin prime average the sum of two twin prime averages, two ways?

primes of the form 2+pq

Can the sum of squares of odd primes equal the square of an odd prime?

A corollary of Brun's pure sieve from Opera de Cribro by Friedlander and Iwaniec

Can we write down a formula for the simultaneous images of the $C_q$?

Potential progress concerning the twin prime conjecture

New method to generate twin primes.

$A(x) = \prod_{p,q \in \Bbb{P}} (1 - \frac{x^2 - 1}{pq}) = 0$ if and only if $x$ is a twin prime average?

$n+1$ and $n \phi (n) + 1$ are both perfect squares if and only if $n$ is a product of twin primes?

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