Question

Is there any approach proof for Legendre conjecture or it is completed solved?

score 97 · Answer 1 · 2026-04-29 12:51:48

97

Views

Is there any approach proof for Legendre conjecture or it is completed solved?

Published on 29 Apr 2026 - 12:51

score 734 · Answer 2 · 2026-04-29 12:07:56

734

Views

Conjectures Disproven by the use of Computers?

Published on 29 Apr 2026 - 12:07

score 369 · Answer 3 · 2026-04-29 12:52:21

369

Views

How large will the smallest counter-example probably be?

Published on 29 Apr 2026 - 12:52

score 67 · Answer 4 · 2026-05-03 17:39:13

67

Views

On integer sequences of the form $\sum_{n=1}^N (a(n))^2H_n^2,$ where $H_n$ is the $n$th harmonic number: refute my conjecture and add yourself example

Published on 03 May 2026 - 17:39

score 105 · Answer 5 · 2026-04-29 12:44:32

105

Views

For prime numbers $p_n$ it holds $m\equiv p_n^2\pmod {p_{n+1}}\implies$ $m$ is a square

Published on 29 Apr 2026 - 12:44

score 72 · Answer 6 · 2026-04-29 12:44:32

72

Views

All even squares are congruent with a prime square $p_n^2\pmod {p_{n+1}}$

Published on 29 Apr 2026 - 12:44

score 428 · Answer 7 · 2026-04-29 12:44:28

428

Views

On the conjecture that, for every $n$, $\lfloor e^{\frac{p_{n^2}\#}{p_{n^2 + 1}}}\rfloor $ is a square number.

Published on 29 Apr 2026 - 12:44

score 102 · Answer 8 · 2026-04-29 12:52:25

102

Views

A conjecture concerning primes and perhaps prime gaps

Published on 29 Apr 2026 - 12:52

score 197 · Answer 9 · 2026-04-29 12:51:48

197

Views

Does $\operatorname*{\exists}\limits^{\infty} f(n) :$ prime?

Published on 29 Apr 2026 - 12:51

score 246 · Answer 10 · 2026-04-29 12:51:53

246

Views

On a conjecture and other numbers like $144$.

Published on 29 Apr 2026 - 12:51

score 115 · Answer 11 · 2026-04-29 12:52:13

115

Views

On the conjecture that if $\,\forall\{x, y, z\}\subset \Bbb{Z^+}$ squarefree, and $\ x^3 + y^3 = z^2$, then $\gcd(3, x, y) = 1$.

Published on 29 Apr 2026 - 12:52

score 118 · Answer 12 · 2026-04-29 12:52:24

118

Views

A trivial prime conjecture?

Published on 29 Apr 2026 - 12:52

score 315 · Answer 13 · 2026-04-29 12:52:22

315

Views

Compositeness tests for specific classes of generalized repunit numbers

Published on 29 Apr 2026 - 12:52

score 140 · Answer 14 · 2026-04-29 12:51:53

140

Views

A remarkable(?) condition on sequences of natural numbers

Published on 29 Apr 2026 - 12:51

score 121 · Answer 15 · 2026-04-29 12:51:51

121

Views

The asymptotic of $\sum_{1\leq n\leq x}\frac{\sum_{k\leq n}\mu(k)}{n\cdot\operatorname{rad}(n)}\log\left(\frac{x}{n}\right)$ versus conjectures

Published on 29 Apr 2026 - 12:51

List Question

Is there any approach proof for Legendre conjecture or it is completed solved?

Conjectures Disproven by the use of Computers?

How large will the smallest counter-example probably be?

On integer sequences of the form $\sum_{n=1}^N (a(n))^2H_n^2,$ where $H_n$ is the $n$th harmonic number: refute my conjecture and add yourself example

For prime numbers $p_n$ it holds $m\equiv p_n^2\pmod {p_{n+1}}\implies$ $m$ is a square

All even squares are congruent with a prime square $p_n^2\pmod {p_{n+1}}$

On the conjecture that, for every $n$, $\lfloor e^{\frac{p_{n^2}\#}{p_{n^2 + 1}}}\rfloor $ is a square number.

A conjecture concerning primes and perhaps prime gaps

Does $\operatorname*{\exists}\limits^{\infty} f(n) :$ prime?

On a conjecture and other numbers like $144$.

On the conjecture that if $\,\forall\{x, y, z\}\subset \Bbb{Z^+}$ squarefree, and $\ x^3 + y^3 = z^2$, then $\gcd(3, x, y) = 1$.

A trivial prime conjecture?

Compositeness tests for specific classes of generalized repunit numbers

A remarkable(?) condition on sequences of natural numbers

The asymptotic of $\sum_{1\leq n\leq x}\frac{\sum_{k\leq n}\mu(k)}{n\cdot\operatorname{rad}(n)}\log\left(\frac{x}{n}\right)$ versus conjectures

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