Question

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

score 93 · Answer 1 · 2018-02-06 13:28:33

93

Views

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

Published on 06 Feb 2018 - 13:28

score 726 · Answer 2 · 2026-03-22 15:57:38

726

Views

Conjectures Disproven by the use of Computers?

Published on 22 Mar 2026 - 15:57

score 363 · Answer 3 · 2018-02-08 12:18:06

363

Views

How large will the smallest counter-example probably be?

Published on 08 Feb 2018 - 12:18

score 59 · Answer 4 · 2026-03-22 19:50:36

59

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 22 Mar 2026 - 19:50

score 99 · Answer 5 · 2026-03-24 23:48:10

99

Views

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

Published on 24 Mar 2026 - 23:48

score 66 · Answer 6 · 2026-03-25 01:17:32

66

Views

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

Published on 25 Mar 2026 - 1:17

score 421 · Answer 7 · 2026-03-17 06:01:52

421

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 17 Mar 2026 - 6:01

score 97 · Answer 8 · 2026-03-23 11:46:42

97

Views

A conjecture concerning primes and perhaps prime gaps

Published on 23 Mar 2026 - 11:46

score 194 · Answer 9 · 2026-03-24 23:44:22

194

Views

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

Published on 24 Mar 2026 - 23:44

score 243 · Answer 10 · 2026-03-25 01:23:56

243

Views

On a conjecture and other numbers like $144$.

Published on 25 Mar 2026 - 1:23

score 111 · Answer 11 · 2018-02-15 12:37:43

111

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 15 Feb 2018 - 12:37

score 111 · Answer 12 · 2026-03-22 02:24:50

111

Views

A trivial prime conjecture?

Published on 22 Mar 2026 - 2:24

score 310 · Answer 13 · 2018-02-18 12:23:54

310

Views

Compositeness tests for specific classes of generalized repunit numbers

Published on 18 Feb 2018 - 12:23

score 134 · Answer 14 · 2026-03-22 22:00:24

134

Views

A remarkable(?) condition on sequences of natural numbers

Published on 22 Mar 2026 - 22:00

score 117 · Answer 15 · 2018-02-21 10:47:15

117

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 21 Feb 2018 - 10:47

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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