List questions from prime-numbers

Published on 19 Jan 2018 - 5:35

193

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Proof congruence identity modulo $p$: $2^2\cdot4^2\cdot\dots\cdot(p-3)^2\cdot(p-1)^2 \equiv (-1)^{\frac{1}{2}(p+1)}\mod{p}$

Published on 24 Mar 2026 - 15:30

39

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Smallest Cunningham chain of length $4$

Published on 22 Mar 2026 - 10:28

89

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Eisenstein's criterion over polynomials irreducible

Published on 23 Mar 2026 - 3:50

87

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Is there a pattern to addition of primesFactored numbers?

Published on 20 Mar 2026 - 10:45

363

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What will be the difference?

Published on 21 Mar 2026 - 20:53

64

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Sums of positive integers $2$ apart can be every composite number and never a prime.

Published on 21 Mar 2026 - 23:24

237

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How many variations of new primitive Pythagorean triples are there when the hypotenuse is multiplied by a prime?

Published on 19 Mar 2026 - 14:10

251

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A variation on Giuga's conjecture

Published on 20 Mar 2026 - 12:30

890

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Fibonacci numbers mod $p$

Published on 21 Mar 2026 - 10:54

346

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Explanation of prime gap result

Published on 22 Mar 2026 - 8:09

352

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Does every sequence of digits occur in one of the primes

Published on 22 Mar 2026 - 20:02

72

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What's the pattern to $\frac12(m+1)(2n+3m)$ for positive $n$, $m$?

Published on 14 Mar 2026 - 11:46

141

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The behaviour of $\sum_{\mathcal{R}\leq x}\left\{\frac{x}{\mathcal{R}}\right\}$, where $\mathcal{R}$ denote Ramanujan primes

Published on 22 Mar 2026 - 7:53

94

Views

Proof verification: Let $p\geq 2$. If $2^{p}-1$ is prime, then $p$ must also be prime.

Published on 22 Jan 2018 - 4:58

List Question

Show n+1th prime of a given form less than prime of given form

Proof congruence identity modulo $p$: $2^2\cdot4^2\cdot\dots\cdot(p-3)^2\cdot(p-1)^2 \equiv (-1)^{\frac{1}{2}(p+1)}\mod{p}$

Smallest Cunningham chain of length $4$

Eisenstein's criterion over polynomials irreducible

Is there a pattern to addition of primesFactored numbers?

What will be the difference?

Sums of positive integers $2$ apart can be every composite number and never a prime.

How many variations of new primitive Pythagorean triples are there when the hypotenuse is multiplied by a prime?

A variation on Giuga's conjecture

Fibonacci numbers mod $p$

Explanation of prime gap result

Does every sequence of digits occur in one of the primes

What's the pattern to $\frac12(m+1)(2n+3m)$ for positive $n$, $m$?

The behaviour of $\sum_{\mathcal{R}\leq x}\left\{\frac{x}{\mathcal{R}}\right\}$, where $\mathcal{R}$ denote Ramanujan primes

Proof verification: Let $p\geq 2$. If $2^{p}-1$ is prime, then $p$ must also be prime.

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