Question

Is there a proof of infinitely many primes $p$ such that $2^p-1$ is composite

score 613 · Answer 1 · 2016-09-15 14:20:03

613

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Is there a proof of infinitely many primes $p$ such that $2^p-1$ is composite

Published on 15 Sep 2016 - 14:20

score 176 · Answer 2 · 2016-09-18 07:30:26

176

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A general criterion of convergence of series?

Published on 18 Sep 2016 - 7:30

score 49 · Answer 3 · 2016-09-19 10:38:30

49

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Conjecture: if $a_{n+1}-a_{n}=c $ $\forall n\in\mathbb{N}$ and $b_{n+1}-b_{n} \rightarrow \infty$ then $a_{n}/b_{n} \rightarrow 0$

Published on 19 Sep 2016 - 10:38

score 131 · Answer 4 · 2016-09-19 21:19:03

131

Views

A conjecture on tensor product vectors

Published on 19 Sep 2016 - 21:19

score 578 · Answer 5 · 2016-09-22 15:33:01

578

Views

Conjecture $\sum_{n=1}^\infty\frac{n^2}{(-1)^n \cosh(\pi n\sqrt{3})-1}=\frac{1}{12\pi^2}$

Published on 22 Sep 2016 - 15:33

score 4.3k · Answer 6 · 2026-03-25 07:44:02

4.3k

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Is any mathematican more famous for their conjecture(s) than their theorem(s)?

Published on 25 Mar 2026 - 7:44

score 142 · Answer 7 · 2016-09-24 04:55:22

142

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How to show this conjecture：$\frac{1}{\sqrt{a_{1}}}+\frac{1}{\sqrt{a_{2}}}+\cdots+\frac{1}{\sqrt{a_{n}}}\ge\frac{2n}{\sqrt{a_{1}}+\sqrt{a_{n}}}$

Published on 24 Sep 2016 - 4:55

score 63 · Answer 8 · 2016-09-25 15:47:17

63

Views

$S_n=\sum^n_{k=1} (-1)^{\Omega(q_k)}\cdot{q_k}$ change sign infinitely many times?

Published on 25 Sep 2016 - 15:47

score 1.7k · Answer 9 · 2016-09-28 03:31:25

1.7k

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What all are still Unproven Conjectures in Number Theory

Published on 28 Sep 2016 - 3:31

score 72 · Answer 10 · 2026-03-25 09:50:16

72

Views

A variant of the radical for integers and the abc-conjecture

Published on 25 Mar 2026 - 9:50

score 7k · Answer 11 · 2026-03-25 11:30:27

7k

Views

What is the state of Carmichael's totient function conjecture?

Published on 25 Mar 2026 - 11:30

score 42 · Answer 12 · 2026-03-25 10:57:20

42

Views

Does a basis $b$ exist such that only a finite number of palindromes in base $b$ are primes?

Published on 25 Mar 2026 - 10:57

score 702 · Answer 13 · 2016-10-21 16:23:29

702

Views

Solving a high school conjecture

Published on 21 Oct 2016 - 16:23

score 512 · Answer 14 · 2026-03-25 14:32:23

512

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A Generalization of Goldbach’s Conjecture

Published on 25 Mar 2026 - 14:32

score 680 · Answer 15 · 2026-03-25 22:25:59

680

Views

Complete monotonicity of a sequence related to tetration

Published on 25 Mar 2026 - 22:25

List Question

Is there a proof of infinitely many primes $p$ such that $2^p-1$ is composite

A general criterion of convergence of series?

Conjecture: if $a_{n+1}-a_{n}=c $ $\forall n\in\mathbb{N}$ and $b_{n+1}-b_{n} \rightarrow \infty$ then $a_{n}/b_{n} \rightarrow 0$

A conjecture on tensor product vectors

Conjecture $\sum_{n=1}^\infty\frac{n^2}{(-1)^n \cosh(\pi n\sqrt{3})-1}=\frac{1}{12\pi^2}$

Is any mathematican more famous for their conjecture(s) than their theorem(s)?

How to show this conjecture：$\frac{1}{\sqrt{a_{1}}}+\frac{1}{\sqrt{a_{2}}}+\cdots+\frac{1}{\sqrt{a_{n}}}\ge\frac{2n}{\sqrt{a_{1}}+\sqrt{a_{n}}}$

$S_n=\sum^n_{k=1} (-1)^{\Omega(q_k)}\cdot{q_k}$ change sign infinitely many times?

What all are still Unproven Conjectures in Number Theory

A variant of the radical for integers and the abc-conjecture

What is the state of Carmichael's totient function conjecture?

Does a basis $b$ exist such that only a finite number of palindromes in base $b$ are primes?

Solving a high school conjecture

A Generalization of Goldbach’s Conjecture

Complete monotonicity of a sequence related to tetration

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