# Inspired by Finn Hulse

I was inspired by this little problem, which I got wrong because I was missing a tiny term in the sum.

So, I pose this question:

Approximate the number of semiprimes less than $$e^{100}$$.

My approximation is

$8.09350340 \ldots \times 10^{41}$

It's really messy and pretty tedious but involves simple calculus and algebra. The estimate is the upper bound of a lower bound.

Note by Jake Lai
3 years, 4 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

Thanks for the mention. :D

- 3 years, 4 months ago

@Jake Lai Sorry for the mistake. I have edited that problem. I could not reply there I think there is some bug. :)

- 3 years, 2 months ago

By "upper bound of a lower bound", do you mean the "greatest lower bound"?

Staff - 3 years, 4 months ago

No, because I don't know if it is the greatest lower bound. All I know is that the lower bound is greater than it's "supposed" to be. This is because I ignored a $$\ln \ln x$$ term in an integral I was dealing with.

- 3 years, 4 months ago

Cheers for the inspiration, @Finn Hulse. Hope you find this fun.

- 3 years, 4 months ago