List questions from prime-numbers

Published on 13 Apr 2026 - 6:47

199

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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 29 Apr 2026 - 12:23

42

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Smallest Cunningham chain of length $4$

Published on 13 Apr 2026 - 21:08

98

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Eisenstein's criterion over polynomials irreducible

Published on 03 May 2026 - 8:22

95

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Is there a pattern to addition of primesFactored numbers?

Published on 02 May 2026 - 18:33

375

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What will be the difference?

Published on 07 May 2026 - 6:12

65

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

Published on 25 Mar 2026 - 1:20

246

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

Published on 07 May 2026 - 13:19

260

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A variation on Giuga's conjecture

Published on 04 May 2026 - 2:11

899

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Fibonacci numbers mod $p$

Published on 10 May 2026 - 9:32

349

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Explanation of prime gap result

Published on 11 Apr 2026 - 13:21

360

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Does every sequence of digits occur in one of the primes

Published on 03 May 2026 - 17:37

73

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

Published on 25 Mar 2026 - 3:02

152

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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 07 May 2026 - 11:34

97

Views

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

Published on 15 Apr 2026 - 6:25

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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