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Easy proof of a weak form of Mertens's second theorem

score 1.1k · Answer 1 · 2026-03-25 15:42:18

1.1k

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Easy proof of a weak form of Mertens's second theorem

Published on 25 Mar 2026 - 15:42

score 56 · Answer 2 · 2026-03-22 23:16:36

56

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Is feasible a simple inequality as a combination of the Firoozbakht's conjecture and the properties of the Ramanujan tau function?

Published on 22 Mar 2026 - 23:16

score 108 · Answer 3 · 2026-03-22 21:30:25

108

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Is there any pseudoprime, $p$ such that $p\not\equiv\pm{1\bmod{18}}$?

Published on 22 Mar 2026 - 21:30

score 84 · Answer 4 · 2026-03-25 15:17:51

84

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Proving maximal ideals of $\mathbb{Z}[x]$ contain a prime

Published on 25 Mar 2026 - 15:17

score 362 · Answer 5 · 2018-03-06 21:42:17

362

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Proof by induction (Chinese remainder theorem?)

Published on 06 Mar 2018 - 21:42

score 48 · Answer 6 · 2018-03-07 00:03:12

48

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Number of primes that can divide ...

Published on 07 Mar 2018 - 0:03

score 81 · Answer 7 · 2026-03-25 01:18:56

81

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Given a set of primes S, show that no prime in S divides the sum of staggered products of these primes.

Published on 25 Mar 2026 - 1:18

score 197 · Answer 8 · 2026-03-25 06:30:19

197

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Let $p$ be a prime number. Prove that there exists $x∈Z$ for which $p|x^2−x+ 3$ if and only if there exists $y∈Z$ for which $p|y^2−y+ 25$.

Published on 25 Mar 2026 - 6:30

score 396 · Answer 9 · 2018-03-07 14:12:26

396

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A conjecture involving the sum of the squares of prime factors

Published on 07 Mar 2018 - 14:12

score 45 · Answer 10 · 2018-03-07 20:51:38

45

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Can we prove that for some $k$ we have the following inequality?

Published on 07 Mar 2018 - 20:51

score 215 · Answer 11 · 2026-03-23 01:50:23

215

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Ratios of prime gaps $(p_{n+1}-p_n)/(p_{2n+1}-p_{2n})$

Published on 23 Mar 2026 - 1:50

score 81 · Answer 12 · 2026-03-25 13:34:19

81

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What about a lower and an upper bound of $\log |\sin N_n|$, where $N_n$ is the primorial of order $n$?

Published on 25 Mar 2026 - 13:34

score 282 · Answer 13 · 2018-03-08 06:30:01

282

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It is given that $p = 2q+1$, and $p$ is a prime number. Prove that $(q!)^2 +(-1)^q$ is a multiple of $p$.

Published on 08 Mar 2018 - 6:30

score 1.8k · Answer 14 · 2018-03-08 06:41:44

1.8k

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How many very quiteprime positive integers are there less than 90000?

Published on 08 Mar 2018 - 6:41

score 291 · Answer 15 · 2018-03-08 11:02:40

291

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The arithmetic sequence of 4 prime numbers

Published on 08 Mar 2018 - 11:02

List Question

Easy proof of a weak form of Mertens's second theorem

Is feasible a simple inequality as a combination of the Firoozbakht's conjecture and the properties of the Ramanujan tau function?

Is there any pseudoprime, $p$ such that $p\not\equiv\pm{1\bmod{18}}$?

Proving maximal ideals of $\mathbb{Z}[x]$ contain a prime

Proof by induction (Chinese remainder theorem?)

Number of primes that can divide ...

Given a set of primes S, show that no prime in S divides the sum of staggered products of these primes.

Let $p$ be a prime number. Prove that there exists $x∈Z$ for which $p|x^2−x+ 3$ if and only if there exists $y∈Z$ for which $p|y^2−y+ 25$.

A conjecture involving the sum of the squares of prime factors

Can we prove that for some $k$ we have the following inequality?

Ratios of prime gaps $(p_{n+1}-p_n)/(p_{2n+1}-p_{2n})$

What about a lower and an upper bound of $\log |\sin N_n|$, where $N_n$ is the primorial of order $n$?

It is given that $p = 2q+1$, and $p$ is a prime number. Prove that $(q!)^2 +(-1)^q$ is a multiple of $p$.

How many very quiteprime positive integers are there less than 90000?

The arithmetic sequence of 4 prime numbers

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