Question

Is this observation equivalent to Legendre's conjecture? $\forall n \in \Bbb N^+, \exists k \in \Bbb N^+:\ \ (n^2)\# \lt k! \lt (n+1)^2\#$

score 221 · Answer 1 · 2026-03-25 10:59:03

221

Views

Is this observation equivalent to Legendre's conjecture? $\forall n \in \Bbb N^+, \exists k \in \Bbb N^+:\ \ (n^2)\# \lt k! \lt (n+1)^2\#$

Published on 25 Mar 2026 - 10:59

score 242 · Answer 2 · 2026-03-26 08:02:23

242

Views

Does make sense a generalization of Lagarias equivalence with $H_n^s=1+1/2^s+\ldots+1/n^s$ and $\sigma^s(n)=\sum_{k\mid n}k^s$, for $\Re s>1$?

Published on 26 Mar 2026 - 8:02

score 200 · Answer 3 · 2016-08-20 04:57:37

200

Views

A conjecture about integer polynomials and primes

Published on 20 Aug 2016 - 4:57

score 93 · Answer 4 · 2026-03-27 03:46:01

93

Views

A conjecture about primes and holomorphic functions

Published on 27 Mar 2026 - 3:46

score 261 · Answer 5 · 2016-08-21 22:34:13

261

Views

An accountancy of the natural numbers

Published on 21 Aug 2016 - 22:34

score 145 · Answer 6 · 2016-08-23 10:56:38

145

Views

Rearrange convergent series

Published on 23 Aug 2016 - 10:56

score 233 · Answer 7 · 2016-08-24 17:44:10

233

Views

A series with the non square free numbers $q_n:\:$ $\sum_{k=1}^\infty\frac{(-1)^{1+\Omega(q_k)}}{q_k}=0$

Published on 24 Aug 2016 - 17:44

score 327 · Answer 8 · 2026-03-25 09:47:07

327

Views

A conjecture with connection to the $abc$-conjecture

Published on 25 Mar 2026 - 9:47

score 248 · Answer 9 · 2026-03-25 09:48:57

248

Views

Conjecture: injection from exceptional abc-triplets to natural numbers

Published on 25 Mar 2026 - 9:48

score 93 · Answer 10 · 2016-08-31 17:26:46

93

Views

$P^2 + P + 1$ is prime if $P$ is prime.

Published on 31 Aug 2016 - 17:26

score 108 · Answer 11 · 2016-09-11 18:55:30

108

Views

Who is credited with the conjecture that all odd squares are solitary?

Published on 11 Sep 2016 - 18:55

score 68 · Answer 12 · 2026-03-26 07:38:52

68

Views

If $N = q^k n^2$ is an odd perfect number with Euler prime $q$, does the following implication hold?

Published on 26 Mar 2026 - 7:38

score 156 · Answer 13 · 2016-09-12 10:21:31

156

Views

Irrationality of the Riemann zeta-function on odd arguments

Published on 12 Sep 2016 - 10:21

score 60 · Answer 14 · 2016-09-14 12:55:00

60

Views

A property of v

Published on 14 Sep 2016 - 12:55

score 400 · Answer 15 · 2026-03-26 07:35:40

400

Views

On the undecidability of the existence of odd perfect numbers

Published on 26 Mar 2026 - 7:35

List Question

Is this observation equivalent to Legendre's conjecture? $\forall n \in \Bbb N^+, \exists k \in \Bbb N^+:\ \ (n^2)\# \lt k! \lt (n+1)^2\#$

Does make sense a generalization of Lagarias equivalence with $H_n^s=1+1/2^s+\ldots+1/n^s$ and $\sigma^s(n)=\sum_{k\mid n}k^s$, for $\Re s>1$?

A conjecture about integer polynomials and primes

A conjecture about primes and holomorphic functions

An accountancy of the natural numbers

Rearrange convergent series

A series with the non square free numbers $q_n:\:$ $\sum_{k=1}^\infty\frac{(-1)^{1+\Omega(q_k)}}{q_k}=0$

A conjecture with connection to the $abc$-conjecture

Conjecture: injection from exceptional abc-triplets to natural numbers

$P^2 + P + 1$ is prime if $P$ is prime.

Who is credited with the conjecture that all odd squares are solitary?

If $N = q^k n^2$ is an odd perfect number with Euler prime $q$, does the following implication hold?

Irrationality of the Riemann zeta-function on odd arguments

A property of v

On the undecidability of the existence of odd perfect numbers

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