Question

A slight generalization of the Sieve of Sundaram that might shed light on the $6n \pm 1$ phenomenon of sequence A002822.

score 169 · Answer 1 · 2026-03-26 09:18:07

169

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A slight generalization of the Sieve of Sundaram that might shed light on the $6n \pm 1$ phenomenon of sequence A002822.

Published on 26 Mar 2026 - 9:18

score 103 · Answer 2 · 2021-05-11 13:28:59

103

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Generating new prime number by adding $40$ to larger number of twin primes

Published on 11 May 2021 - 13:28

score 142 · Answer 3 · 2021-05-19 04:43:34

142

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Why are some numbers "paired" in their prime distribution

Published on 19 May 2021 - 4:43

score 150 · Answer 4 · 2021-05-25 13:55:10

150

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Related to the sum of consecutive primes

Published on 25 May 2021 - 13:55

score 100 · Answer 5 · 2026-03-26 09:18:05

100

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Alternating sum of the reciprocals of the twin primes $\sum(\frac1p-\frac1{p+2})$

Published on 26 Mar 2026 - 9:18

score 567 · Answer 6 · 2021-06-04 09:09:54

567

Views

What does it mean if the twin prime conjecture is true or false?

Published on 04 Jun 2021 - 9:09

score 161 · Answer 7 · 2026-03-26 06:42:46

161

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Is it possible that every $P$ as a prime number, can be expressed as a prime factor of $E$ such that $E$ is the sum of a pair of twin primes?

Published on 26 Mar 2026 - 6:42

score 55 · Answer 8 · 2021-07-15 02:26:08

55

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Successive intervals bounded by numbers of the form $(6k+1)^2$ contain (approximately) equal numbers of twin primes

Published on 15 Jul 2021 - 2:26

score 211 · Answer 9 · 2021-07-19 14:14:04

211

Views

Full set of congruences uniquely defining all twin primes

Published on 19 Jul 2021 - 14:14

score 205 · Answer 10 · 2021-08-10 01:57:47

205

Views

For twin primes $p$ and $q$, prove there is an integer $a$ such that $p|(a^2-q)$ if and only if there is an integer $b$ such that $q|(b^2-p)$.

Published on 10 Aug 2021 - 1:57

score 187 · Answer 11 · 2021-08-10 18:37:26

187

Views

Observation about twin primes: is it true? If so, why?

Published on 10 Aug 2021 - 18:37

score 165 · Answer 12 · 2021-09-16 23:31:28

165

Views

Potential infinite, fast growing subsequence of twin primes

Published on 16 Sep 2021 - 23:31

score 79 · Answer 13 · 2026-03-25 14:25:17

79

Views

Is there a formula for $|H_n|$, where $H_n = \{ $ units $u \pmod n$ such that $u^n = u, \}$ is the group of $(n-1)$th roots of unity modulo $n$?

Published on 25 Mar 2026 - 14:25

score 142 · Answer 14 · 2021-10-19 02:33:29

142

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$H(n)=\lfloor\dfrac{b}{n}\rfloor- \lfloor \dfrac{a}{n} \rfloor=$ (roughly) # odd pairs $o, o+2 \in [a,b]$ such that $n \mid o$ or $n \mid o+2$

Published on 19 Oct 2021 - 2:33

score 128 · Answer 15 · 2021-10-19 14:37:30

128

Views

Can the prime counting function possibly satisfy this functional equation?

Published on 19 Oct 2021 - 14:37

List Question

A slight generalization of the Sieve of Sundaram that might shed light on the $6n \pm 1$ phenomenon of sequence A002822.

Generating new prime number by adding $40$ to larger number of twin primes

Why are some numbers "paired" in their prime distribution

Related to the sum of consecutive primes

Alternating sum of the reciprocals of the twin primes $\sum(\frac1p-\frac1{p+2})$

What does it mean if the twin prime conjecture is true or false?

Is it possible that every $P$ as a prime number, can be expressed as a prime factor of $E$ such that $E$ is the sum of a pair of twin primes?

Successive intervals bounded by numbers of the form $(6k+1)^2$ contain (approximately) equal numbers of twin primes

Full set of congruences uniquely defining all twin primes

For twin primes $p$ and $q$, prove there is an integer $a$ such that $p|(a^2-q)$ if and only if there is an integer $b$ such that $q|(b^2-p)$.

Observation about twin primes: is it true? If so, why?

Potential infinite, fast growing subsequence of twin primes

Is there a formula for $|H_n|$, where $H_n = \{ $ units $u \pmod n$ such that $u^n = u, \}$ is the group of $(n-1)$th roots of unity modulo $n$?

$H(n)=\lfloor\dfrac{b}{n}\rfloor- \lfloor \dfrac{a}{n} \rfloor=$ (roughly) # odd pairs $o, o+2 \in [a,b]$ such that $n \mid o$ or $n \mid o+2$

Can the prime counting function possibly satisfy this functional equation?

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