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.

#NumberTheory #Primes #Analysis #Approximation #Semiprimes

Easy Math Editor

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`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`	$\sum_{i=1}^3$
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Comments

Thanks for the mention. :D

Finn Hulse - 6 years, 3 months ago

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

Jake Lai - 6 years, 3 months ago

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

Calvin Lin Staff - 6 years, 3 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.

Jake Lai - 6 years, 3 months ago

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

Rajdeep Dhingra - 6 years, 1 month ago

Math	Appears 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}`	$\boxed{123}$