Newbetuts

Prove $_4F_3(1/8,3/8,5/8,7/8;1/4,1/2,3/4;1/2)=\frac{\sqrt{2-\sqrt2+\sqrt{2-\sqrt2}}+\sqrt{2+\sqrt2+\sqrt{2+\sqrt2}}}{2\,\sqrt2}$

Solving a high school conjecture

Does the following lower bound improve on $I(q^k) + I(n^2) > 3 - \frac{q-2}{q(q-1)}$, where $q^k n^2$ is an odd perfect number? - Part II

A condition for being a prime: $\;\forall m,n\in\mathbb Z^+\!:\,p=m+n\implies \gcd(m,n)=1$

A conjecture about an unlimited path

Conjecture: "For every prime $k$ there will be at least one prime of the form $n! \pm k$" true?

The Goldbach Conjecture and Hardy-Littlewood Asymptotic

a conjectured continued-fraction for $\displaystyle\cot\left(\frac{z\pi}{4z+2n}\right)$ that leads to a new limit for $\pi$

The four runner problem/conjecture

A conjecture concerning primes and algebra

Can composition of integer polynomial and rational polynomial with a non-integer coefficient result in integer polynomial?

Conjecture $\int_0^1\frac{\ln\left(\ln^2x+\arccos^2x\right)}{\sqrt{1-x^2}}dx\stackrel?=\pi\,\ln\ln2$

Can this bound for the abundancy index of $n$ be improved, given that $q^k n^2$ is an odd perfect number with $k=1$?

Density of odd numbers in a sequence relating base 2 and base 3 expansion

A curious infinite product of factorials

How to prove $_2F_1\big(\tfrac16,\tfrac16;\tfrac23;-2^7\phi^9\big)=\large \frac{3}{5^{5/6}}\,\phi^{-1}\,$ with golden ratio $\phi$?

New posts in conjectures

Adding digits in this way to primes to obtain another primes

For any $k \gt 1$, if $n!+k$ is a square then will $n \le k$ always be true?

Are there infinitely many primes $p$ such that $\frac{(p-1)! +1}{p}$ is prime?

Yet another conjecture about primes

Prove $_4F_3(1/8,3/8,5/8,7/8;1/4,1/2,3/4;1/2)=\frac{\sqrt{2-\sqrt2+\sqrt{2-\sqrt2}}+\sqrt{2+\sqrt2+\sqrt{2+\sqrt2}}}{2\,\sqrt2}$

Solving a high school conjecture

Does the following lower bound improve on $I(q^k) + I(n^2) > 3 - \frac{q-2}{q(q-1)}$, where $q^k n^2$ is an odd perfect number? - Part II

A condition for being a prime: $\;\forall m,n\in\mathbb Z^+\!:\,p=m+n\implies \gcd(m,n)=1$

A conjecture about an unlimited path

Conjecture: "For every prime $k$ there will be at least one prime of the form $n! \pm k$" true?

The Goldbach Conjecture and Hardy-Littlewood Asymptotic

a conjectured continued-fraction for $\displaystyle\cot\left(\frac{z\pi}{4z+2n}\right)$ that leads to a new limit for $\pi$

The four runner problem/conjecture

A conjecture concerning primes and algebra

Can composition of integer polynomial and rational polynomial with a non-integer coefficient result in integer polynomial?

Conjecture $\int_0^1\frac{\ln\left(\ln^2x+\arccos^2x\right)}{\sqrt{1-x^2}}dx\stackrel?=\pi\,\ln\ln2$

Can this bound for the abundancy index of $n$ be improved, given that $q^k n^2$ is an odd perfect number with $k=1$?

Density of odd numbers in a sequence relating base 2 and base 3 expansion

A curious infinite product of factorials

How to prove $_2F_1\big(\tfrac16,\tfrac16;\tfrac23;-2^7\phi^9\big)=\large \frac{3}{5^{5/6}}\,\phi^{-1}\,$ with golden ratio $\phi$?