Question

On a conjecture that if $2\left(p_n+p_{n-1}\right)\equiv -1\pmod {n^2}$ then $n=11$ only.

score 104 · Answer 1 · 2026-04-16 23:11:33

104

Views

On a conjecture that if $2\left(p_n+p_{n-1}\right)\equiv -1\pmod {n^2}$ then $n=11$ only.

Published on 16 Apr 2026 - 23:11

score 259 · Answer 2 · 2026-04-10 18:15:15

259

Views

Is $387420547$ another counter example to John H. Conway's Problem $5$?

Published on 10 Apr 2026 - 18:15

score 30 · Answer 3 · 2026-05-10 15:09:00

30

Views

Questions regarding equations that involve arithmetic functions, and odd integers being deficient or perfect

Published on 10 May 2026 - 15:09

score 84 · Answer 4 · 2026-05-10 15:09:54

84

Views

Confirmation of Proof: $\pi_n + p_a + p_b \geqslant \sum_{i=1}^4 x_i$.

Published on 10 May 2026 - 15:09

score 205 · Answer 5 · 2026-05-10 13:26:23

205

Views

Do odd numbers $n$ satisfying $\gcd(n, \sigma(n)) > \sqrt{n}$ have a special form?

Published on 10 May 2026 - 13:26

score 94 · Answer 6 · 2026-05-10 16:34:57

94

Views

Is $N^n(p_n\#)-p_n\#$ always prime for all $n\in\mathbb{N}_{>1}$?

Published on 10 May 2026 - 16:34

score 254 · Answer 7 · 2026-04-15 19:09:03

254

Views

Is this integral $\int_0^\infty\frac{\cos(a x+ 2b \arctan x)}{x^2+1}dx$ exactly zero when $b\in\mathbb{N}$?

Published on 15 Apr 2026 - 19:09

score 700 · Answer 8 · 2026-05-10 14:56:02

700

Views

Is it true that $2^{2^{n}}$ always ends in the digit $6$?

Published on 10 May 2026 - 14:56

score 793 · Answer 9 · 2026-05-10 17:30:06

793

Views

Is my proof correct on how $k$ must be a power of $2$? Are there other proofs?

Published on 10 May 2026 - 17:30

score 417 · Answer 10 · 2026-04-17 11:55:31

417

Views

Does the prime sequence satisfy $p_n+p_m \le p_{n+m} < p_n p_m$?

Published on 17 Apr 2026 - 11:55

score 165 · Answer 11 · 2026-04-16 21:56:24

165

Views

Conjectured inequality: $\frac{p_{2n+1}-1}{2}\geqslant p_{n+1}+2(n+1)^{2/(n-1)}+\frac12\log_{4}^2(n-6)\qquad(n>6)$

Published on 16 Apr 2026 - 21:56

score 87 · Answer 12 · 2026-04-15 16:05:00

87

Views

Is $\sum_{i=1}^{n-1}i^{n-1}\equiv -1\pmod {2n}\Leftrightarrow \text{$n$ is prime }\equiv 3\pmod 4$?

Published on 15 Apr 2026 - 16:05

score 956 · Answer 13 · 2026-05-10 15:24:19

956

Views

Conways 99 graph problem

Published on 10 May 2026 - 15:24

score 94 · Answer 14 · 2026-04-21 03:15:12

94

Views

On a conjecture that $P_n^{\,2}+5^2+2^k=(P_n-1)^2+l^2$.

Published on 21 Apr 2026 - 3:15

score 221 · Answer 15 · 2026-04-09 16:30:46

221

Views

Approaches to Brocard's problem

Published on 09 Apr 2026 - 16:30

List Question

On a conjecture that if $2\left(p_n+p_{n-1}\right)\equiv -1\pmod {n^2}$ then $n=11$ only.

Is $387420547$ another counter example to John H. Conway's Problem $5$?

Questions regarding equations that involve arithmetic functions, and odd integers being deficient or perfect

Confirmation of Proof: $\pi_n + p_a + p_b \geqslant \sum_{i=1}^4 x_i$.

Do odd numbers $n$ satisfying $\gcd(n, \sigma(n)) > \sqrt{n}$ have a special form?

Is $N^n(p_n\#)-p_n\#$ always prime for all $n\in\mathbb{N}_{>1}$?

Is this integral $\int_0^\infty\frac{\cos(a x+ 2b \arctan x)}{x^2+1}dx$ exactly zero when $b\in\mathbb{N}$?

Is it true that $2^{2^{n}}$ always ends in the digit $6$?

Is my proof correct on how $k$ must be a power of $2$? Are there other proofs?

Does the prime sequence satisfy $p_n+p_m \le p_{n+m} < p_n p_m$?

Conjectured inequality: $\frac{p_{2n+1}-1}{2}\geqslant p_{n+1}+2(n+1)^{2/(n-1)}+\frac12\log_{4}^2(n-6)\qquad(n>6)$

Is $\sum_{i=1}^{n-1}i^{n-1}\equiv -1\pmod {2n}\Leftrightarrow \text{$n$ is prime }\equiv 3\pmod 4$?

Conways 99 graph problem

On a conjecture that $P_n^{\,2}+5^2+2^k=(P_n-1)^2+l^2$.

Approaches to Brocard's problem

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