Question

For any prime $p_{n}>7$, there is at least as much odd composites before $p_{n}$ than between $p_{n}$ and $p_{n+1}$?

score 57 · Answer 1 · 2022-03-06 10:26:31

57

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For any prime $p_{n}>7$, there is at least as much odd composites before $p_{n}$ than between $p_{n}$ and $p_{n+1}$?

Published on 06 Mar 2022 - 10:26

score 59 · Answer 2 · 2022-03-13 20:42:04

59

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The sets $\mathcal{F}_d(m,n,k) = \Big\{ x \in (m, n) : x^2 = k^2 \pmod d\Big\}$ seem to have relationships with each other. What is their structure?

Published on 13 Mar 2022 - 20:42

score 149 · Answer 3 · 2022-03-20 20:05:11

149

Views

Conjecture: there are more than $\pi(p)$ primes between consecutive prime squares

Published on 20 Mar 2022 - 20:05

score 111 · Answer 4 · 2022-03-21 08:38:16

111

Views

What's so hard about contradiction proofs w.r.t. primes?

Published on 21 Mar 2022 - 8:38

score 130 · Answer 5 · 2022-03-29 03:31:00

130

Views

Conjecture on ordering the first $p^2$ naturals by prime factor count

Published on 29 Mar 2022 - 3:31

score 133 · Answer 6 · 2022-04-03 22:57:01

133

Views

Proof for strict inequality $\pi(ab) > \pi(a)\pi(b)$?

Published on 03 Apr 2022 - 22:57

score 100 · Answer 7 · 2022-04-15 09:19:34

100

Views

Does the following hold as a conjecture for maximum gaps between prime numbers? and can it be proved?

Published on 15 Apr 2022 - 9:19

score 436 · Answer 8 · 2026-02-24 02:16:35

436

Views

No infinite arithmetic progression exists with prime numbers

Published on 24 Feb 2026 - 2:16

score 82 · Answer 9 · 2026-03-26 11:18:20

82

Views

Full derivation inside of twin prime statement in terms of multiplicative arithmetic functions. How can the last formula be rearranged?

Published on 26 Mar 2026 - 11:18

score 107 · Answer 10 · 2022-05-26 16:09:20

107

Views

Why does the ninth successive difference of primes appear to have two distinct groups?

Published on 26 May 2022 - 16:09

score 36 · Answer 11 · 2022-06-25 23:34:22

36

Views

Divisibility into primes quadruples

Published on 25 Jun 2022 - 23:34

score 74 · Answer 12 · 2022-07-05 07:33:02

74

Views

On Erdös's inequality regarding prime gaps

Published on 05 Jul 2022 - 7:33

score 58 · Answer 13 · 2022-07-06 04:07:51

58

Views

Multiple of $15$ between quadruples of primes

Published on 06 Jul 2022 - 4:07

score 235 · Answer 14 · 2022-07-06 08:04:56

235

Views

Confusion on the proof of Erdös's prime gap inequality

Published on 06 Jul 2022 - 8:04

score 104 · Answer 15 · 2022-07-24 02:27:27

104

Views

For every odd prime number $p \gt 3$ there exists another prime number $q \lt p$ such that $p - q = 2^n$ for some $n \geq 1$. Can you prove it?

Published on 24 Jul 2022 - 2:27

List Question

For any prime $p_{n}>7$, there is at least as much odd composites before $p_{n}$ than between $p_{n}$ and $p_{n+1}$?

The sets $\mathcal{F}_d(m,n,k) = \Big\{ x \in (m, n) : x^2 = k^2 \pmod d\Big\}$ seem to have relationships with each other. What is their structure?

Conjecture: there are more than $\pi(p)$ primes between consecutive prime squares

What's so hard about contradiction proofs w.r.t. primes?

Conjecture on ordering the first $p^2$ naturals by prime factor count

Proof for strict inequality $\pi(ab) > \pi(a)\pi(b)$?

Does the following hold as a conjecture for maximum gaps between prime numbers? and can it be proved?

No infinite arithmetic progression exists with prime numbers

Full derivation inside of twin prime statement in terms of multiplicative arithmetic functions. How can the last formula be rearranged?

Why does the ninth successive difference of primes appear to have two distinct groups?

Divisibility into primes quadruples

On Erdös's inequality regarding prime gaps

Multiple of $15$ between quadruples of primes

Confusion on the proof of Erdös's prime gap inequality

For every odd prime number $p \gt 3$ there exists another prime number $q \lt p$ such that $p - q = 2^n$ for some $n \geq 1$. Can you prove it?

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