List questions from prime-numbers

Published on 25 Mar 2026 - 1:18

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Prove the asymptotic probability of numbers being relative prime equals $\frac{6}{\pi^2}$

Published on 23 Mar 2026 - 9:29

693

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Spiral of prime numbers.

Published on 16 Feb 2018 - 14:38

79

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Are there more non-trivial powers of the form $S_p$?

Published on 25 Mar 2026 - 8:11

112

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A trivial prime conjecture?

Published on 25 Mar 2026 - 4:16

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if $p$ and $q$ are successive odd primes and $p + q = 2r$ then $r$ is composite,

Published on 18 Feb 2018 - 4:12

787

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Let $p_n$ denote the $n^{th}$ prime then prove that $p_n<2^n$, where $n≥2$

Published on 18 Feb 2018 - 4:57

311

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Compositeness tests for specific classes of generalized repunit numbers

Published on 25 Mar 2026 - 4:16

93

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Summation of primes

Published on 18 Feb 2018 - 18:33

1.5k

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Factoring rational primes over the Eisenstein integers - when can a prime be written as $j^2+3k^2$?

Published on 19 Mar 2026 - 12:19

80

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Given $x^3-120x+p$, find all $p$ that make the polynomial reducible

Published on 19 Feb 2018 - 15:13

1.1k

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What does the notation $q^k || n$ mean?

Published on 19 Feb 2018 - 15:13

241

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Proving $p_{n+1}<p_n^2$ without Bertrand's postulate

Published on 19 Feb 2018 - 17:07

1k

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$\sigma(n) \equiv 1 \space \pmod{n}$ if and only if $n$ is prime

Published on 20 Mar 2026 - 19:46

146

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How to prove that if $n$ is prime then ${{n}\choose{i}} = 0 \mod{n}$?

Published on 22 Mar 2026 - 23:01

List Question

Considering the equation, $6 + (2k+1)\sum_{n=1}^{2k+1}p_n^{ \ \ 3}(-1)^{n+1} = x^2$.

Prove the asymptotic probability of numbers being relative prime equals $\frac{6}{\pi^2}$

Spiral of prime numbers.

Are there more non-trivial powers of the form $S_p$?

A trivial prime conjecture?

if $p$ and $q$ are successive odd primes and $p + q = 2r$ then $r$ is composite,

Let $p_n$ denote the $n^{th}$ prime then prove that $p_n<2^n$, where $n≥2$

Compositeness tests for specific classes of generalized repunit numbers

Summation of primes

Factoring rational primes over the Eisenstein integers - when can a prime be written as $j^2+3k^2$?

Given $x^3-120x+p$, find all $p$ that make the polynomial reducible

What does the notation $q^k || n$ mean?

Proving $p_{n+1}<p_n^2$ without Bertrand's postulate

$\sigma(n) \equiv 1 \space \pmod{n}$ if and only if $n$ is prime

How to prove that if $n$ is prime then ${{n}\choose{i}} = 0 \mod{n}$?

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