List questions from prime-numbers

Published on 21 Mar 2026 - 23:09

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Find all $x \in \mathbb{Z+}$ s.t. $x^2+2x-3$ is prime.

Published on 14 Mar 2026 - 3:25

296

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A congruence involving Lucas polynomials

Published on 20 Mar 2026 - 12:17

51

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Formula for nearest prime $p_x$ less than a number $k$

Published on 17 Mar 2026 - 16:06

839

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what prime numbers can be written as the sum of two consecutive squares?

Published on 28 Jan 2018 - 21:48

87

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Prove an equivalence of modular-arithmetic

Published on 25 Mar 2026 - 1:36

44

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Show that if $p_1$ and $p_2$ are primes such that $p_2 = p_1 + 2$ and $p_1> 3$, then $p_1 + p_2 \equiv 0$ mod $12$

Published on 25 Mar 2026 - 3:22

360

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Is $k^{2018}+2018$ prime for some positive integer $k$ ? If yes, which $k$ is the smallest?

Published on 24 Mar 2026 - 3:49

1.9k

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Created a function with roots at primes and only primes, are there useful applications?

Published on 23 Mar 2026 - 20:47

1k

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Proof: There is no other prime triple then 3,5,7

Published on 24 Mar 2026 - 0:59

167

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Reference for von Koch's 1901 theorem (RH characterization)

Published on 20 Mar 2026 - 21:29

91

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Prime Postulate

Published on 30 Jan 2018 - 20:10

227

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If $x^2-dy^2 = -1$ has a solution in $\mathbb{Z^2}$, then $d$ is the sum of two coprime squares.

Published on 23 Mar 2026 - 4:56

59

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S is the set of all numbers of the form $4n+1$ where $n \geq 1$

Published on 23 Mar 2026 - 7:27

102

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Prove that the set of all prime numbers of the form $6n+5$ is infinite

Published on 22 Mar 2026 - 16:34

List Question

Infinitude of odd primes of the form $4n+3$.

Find all $x \in \mathbb{Z+}$ s.t. $x^2+2x-3$ is prime.

A congruence involving Lucas polynomials

Formula for nearest prime $p_x$ less than a number $k$

what prime numbers can be written as the sum of two consecutive squares?

Prove an equivalence of modular-arithmetic

Show that if $p_1$ and $p_2$ are primes such that $p_2 = p_1 + 2$ and $p_1> 3$, then $p_1 + p_2 \equiv 0$ mod $12$

Is $k^{2018}+2018$ prime for some positive integer $k$ ? If yes, which $k$ is the smallest?

Created a function with roots at primes and only primes, are there useful applications?

Proof: There is no other prime triple then 3,5,7

Reference for von Koch's 1901 theorem (RH characterization)

Prime Postulate

If $x^2-dy^2 = -1$ has a solution in $\mathbb{Z^2}$, then $d$ is the sum of two coprime squares.

S is the set of all numbers of the form $4n+1$ where $n \geq 1$

Prove that the set of all prime numbers of the form $6n+5$ is infinite

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