List questions from prime-numbers

Published on 30 Mar 2026 - 4:56

77

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Since $\lim_{n\to\infty}\pi(n) = \frac{n}{ln(n)}$, can't this be used to prove Legendre’s conjecture?

Published on 15 Feb 2019 - 18:19

428

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Density of integers $n$ with all prime factors of order $O(\log n)$?

Published on 26 Mar 2026 - 6:22

228

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Question related to derived formula for zeta-zero counting function

Published on 25 Mar 2026 - 7:41

862

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Find all primes $p$ for which there are positive integers $x, y$ such that $p+1=2x^2$ and $p^2+1=2y^2$

Published on 16 Feb 2019 - 5:12

207

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"Exceptional" primes greater than 2

Published on 16 Feb 2019 - 12:55

220

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Why Proof of Work is Hard

Published on 25 Mar 2026 - 7:58

103

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What will accepting 1 as prime change?

Published on 18 Feb 2019 - 16:49

107

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Fermat primality test for $a=n-1$

Published on 27 Mar 2026 - 11:27

23

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When is a field element in its base field?

Published on 28 Mar 2026 - 5:57

155

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About gaps between prime numbers

Published on 01 Apr 2026 - 15:40

124

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$p$ is Prime $p \geq 5$ $\implies$ $|\{n^2 \pmod p\mid n \in [0, p-1]\}| = \frac{p+1}{2}$

Published on 01 Apr 2026 - 17:10

151

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Smallest $1\ 000$ digit number $x$ , such that $x$ , $x+2$ and $x+6$ are all prime?

Published on 25 Mar 2026 - 7:45

458

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Are $n^2-1$ and $N$ always relatively prime?

Published on 21 Feb 2019 - 4:18

183

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Amidst $7$ prime numbers, difference of the largest and the smallest prime number is $d$. What is the highest possible value of $d$?

Published on 29 Mar 2026 - 20:21

List Question

Alternate definition of prime numbers

Since $\lim_{n\to\infty}\pi(n) = \frac{n}{ln(n)}$, can't this be used to prove Legendre’s conjecture?

Density of integers $n$ with all prime factors of order $O(\log n)$?

Question related to derived formula for zeta-zero counting function

Find all primes $p$ for which there are positive integers $x, y$ such that $p+1=2x^2$ and $p^2+1=2y^2$

"Exceptional" primes greater than 2

Why Proof of Work is Hard

What will accepting 1 as prime change?

Fermat primality test for $a=n-1$

When is a field element in its base field?

About gaps between prime numbers

$p$ is Prime $p \geq 5$ $\implies$ $|\{n^2 \pmod p\mid n \in [0, p-1]\}| = \frac{p+1}{2}$

Smallest $1\ 000$ digit number $x$ , such that $x$ , $x+2$ and $x+6$ are all prime?

Are $n^2-1$ and $N$ always relatively prime?

Amidst $7$ prime numbers, difference of the largest and the smallest prime number is $d$. What is the highest possible value of $d$?

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