### Questions (265)

 43 Generalizing Ramanujan's proof of Bertrand's Postulate: Can Ramanujan's approach be used to show a prime between $4x$ and $5x$ for $x \ge 3$ 20 Is there a better upper bound for the primorial $x\#$ than $4^x$ 15 Understanding Ramanujan's approach in his proof of Bertrand's Postulate 12 Why is counting the number of least prime factors of a sequence of consecutive integers insufficient to resolve Legendre's Conjecture? 12 Is there a function that can be subtracted from the sum of reciprocals of primes to make the series convergent

### Reputation (3,452)

 +5 Reasoning about $\left(\left\lfloor\frac{2x}{i}\right\rfloor -2\left\lfloor\frac{x}{i}\right\rfloor\right)$ +5 Does $\left\lfloor\frac{x^2+x}{i}\right\rfloor - \left\lfloor\frac{x^2}{i}\right\rfloor = \left\lfloor\frac{x}{i}\right\rfloor$? +5 Upper bound for $\sqrt[n]{n!}$ +5 Reasoning about $x(x+2)$ relatively prime to $\dfrac{p\#}{w}$

 6 How do compare two ratios of gamma functions? 5 Proving that $\pi(2x) < 2 \pi(x)$ 4 Find all positive integers $n$ for some given condition. 3 Infinitely many primes of the form $6n - 1$ 3 Does ABC implies Fermat's last theorem?

### Tags (84)

 14 elementary-number-theory × 151 5 inequality × 45 13 prime-numbers × 131 5 riemann-zeta × 3 12 number-theory × 45 3 factorial × 48 10 gamma-function × 29 3 logarithms × 33 7 analytic-number-theory × 24 3 congruences × 16