New posts in conjectures

Asymptotic frequency of $[0,\,1,\,1]$ in the Thue–Morse sequence

sequences-and-series combinatorics number-theory asymptotics conjectures

Is it true/known/important that $(\log p_n)/n$ is nonincreasing, where $p_n$ is the $n$th odd prime number?

prime-numbers logarithms conjectures

Carmichael number divisible by a given positive integer

elementary-number-theory reference-request conjectures carmichael-numbers

Conjecture about integral $\int_0^1 K\left(\sqrt{\vphantom1x}\right)\,K\left(\sqrt{1-x}\right)\,x^ndx$

definite-integrals special-functions conjectures hypergeometric-function elliptic-integrals

On odd perfect numbers $p^k m^2$ with special prime $p$ satisfying $m^2 - p^k = 2^r t$ - Part II

number-theory inequality conjectures perfect-numbers open-problem

Trigamma identity $4\,\psi_1\!\left(\frac15\right)+\psi_1\!\left(\frac25\right)-\psi_1\!\left(\frac1{10}\right)=\frac{4\pi^2}{\phi\,\sqrt5}.$

calculus special-functions gamma-function conjectures polygamma

Conjecture: Every prime number is the difference between a prime number and a power of $2$

prime-numbers conjectures

Conjecture: For almost all $n$, the sum of $n \bmod k$ for $k<n$ is unique.

elementary-number-theory prime-numbers modular-arithmetic conjectures

Problems with interesting, non-trivial analogues in finite fields

soft-question finite-fields big-list conjectures

Is it true that $\sum_{i=1}^n ( nGx_i^{G} + G^{x_i}) \ge n^2G + G^2n$, for all $x_i>0$, where $G=\prod_{j=1}^nx_j$?

inequality summation conjectures a.m.-g.m.-inequality

All solutions to $1/a+1/b=1/c$?

elementary-number-theory diophantine-equations conjectures

Conjecture about the product of the primitive roots modulo a prime number ($\prod Pr_p$)

elementary-number-theory prime-numbers conjectures primitive-roots

Is there any theoretical indication that this conjecture of Catalan could be true?

number-theory prime-numbers conjectures

Open mathematical questions for which Numerical Search promising

soft-question numerical-methods conjectures

How is moving the last digit of a number to the front and multiplying related to multiplicative orders?

puzzle conjectures multiplicative-order

Does the fraction of distinct substrings in prefixes of the Thue–Morse sequence of length $2^n$ tend to $73/96$?

sequences-and-series discrete-mathematics conjectures experimental-mathematics combinatorics-on-words

An asymptotic series for $\small\prod_{k=n}^\infty\operatorname{sinc}\left({2^{-k}}\pi\right),\,n\to\infty$

asymptotics infinite-product conjectures dirichlet-series experimental-mathematics

Does Diophantine equation $1+n+n^2+\dots+n^k=2m^2$ have a solution for $n,k \geq 2$?

elementary-number-theory diophantine-equations conjectures

Is This a New Property I Have Found Pertaining to Mersenne Primes?

number-theory prime-numbers conjectures primality-test mersenne-numbers

Integrals of the Bessel function $J_0(x)$ over the intervals between its zeros

real-analysis integration asymptotics bessel-functions conjectures