Larry Freeman's user avatar
Larry Freeman's user avatar
Larry Freeman's user avatar
Larry Freeman
  • Member for 9 years, 10 months
  • Last seen this week
48 votes
2 answers
3k views

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 votes
2 answers
3k views

Is there a better upper bound for the primorial $x\#$ than $4^x$

18 votes
0 answers
1k views

Understanding Ramanujan's approach in his proof of Bertrand's Postulate

16 votes
1 answer
897 views

Attempting to restate the question of whether the collatz conjecture has a nontrivial cycle as a combinatorics problem

13 votes
0 answers
294 views

Why is counting the number of least prime factors of a sequence of consecutive integers insufficient to resolve Legendre's Conjecture?

12 votes
1 answer
668 views

Looking for help understanding the Möbius Inversion Formula

12 votes
4 answers
878 views

Is there a function that can be subtracted from the sum of reciprocals of primes to make the series convergent

11 votes
1 answer
172 views

Does it follow that $(n!)^n$ divide $(n^2)!$

11 votes
2 answers
284 views

Question about a function that is a ratio of gamma functions and appears to be strictly increasing for $x\ge 2$

11 votes
1 answer
387 views

What is wrong with this effort to generalize Bertrand's Postulate using the Inclusion-Exclusion Principle

11 votes
0 answers
321 views

Is there an elementary argument for $\prod\limits_{p \le n}p < 3^n$ where $p$ is prime.

10 votes
1 answer
370 views

An alternative proof for Bertrand's Postulate when $n \ge 36$

10 votes
2 answers
462 views

Collatz Conjecture: For a cycle where the maximum odd integer is $x_{max}$, does it follow that $x_{max} < 3^n$

8 votes
1 answer
118 views

Using AM-GM to reason about the upper bound of an $n$th root of a factorial

8 votes
1 answer
406 views

Proving that there are at least $n$ primes between $n$ and $n^2$ for $n \ge 6$

8 votes
1 answer
318 views

Is it possible to generalize Ramanujan's lower bound for factorials that he used in his proof of Bertrand's Postulate?

7 votes
1 answer
627 views

Question about Ramanujan's proof of Bertrand's Postulate

6 votes
2 answers
316 views

Understanding a very elementary property of factorials

6 votes
3 answers
429 views

Is there an integer $y>0$ such that for all $x>y$, at least $4$ of $x+1, x+2, x+3, x+4, x+5$ are divisible by a prime greater than $5$?

6 votes
1 answer
183 views

Paul Erdős showed a simple estimate for $\pi(x) \ge \frac{1}{2}\log_2 x$; is it possible to tweak his argument to improve the estimate?

6 votes
2 answers
198 views

Understanding how to estimate $\pi(x)$ based on Paul Erdos's proof of Bertrand's Postulate

6 votes
1 answer
903 views

Strengthening the Sylvester-Schur Theorem

6 votes
1 answer
80 views

Proving for $a>1,b > 1$, $2^a \ne p^b + 1$

6 votes
1 answer
122 views

What would be the standard way to show for $n \ge 148, \pi(n) < \dfrac{n}{4}$

6 votes
1 answer
164 views

Is this a valid argument for a prime always found between $p_n$ and $2p_n$ when $p_n > 25$

6 votes
0 answers
287 views

The number of distinct least prime factors in a sequence of consecutive integers

6 votes
1 answer
182 views

Why isn't Legendre's Conjecture resolved by the work done by Nair and Hanson in relation to Least Common Multiples?

6 votes
1 answer
534 views

Can $e^{\frac{1}{\ln x}}$ be simplified or roughly approximated

6 votes
1 answer
124 views

Collatz Conjecture: Is this the following a property of the minimum odd integer in a cycle

5 votes
0 answers
246 views

Are these well known properties of binomial coefficients?

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