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# 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
2 years, 11 months ago

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Thanks for the mention. :D

- 2 years, 11 months ago

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

- 2 years, 10 months ago

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

Staff - 2 years, 11 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.

- 2 years, 11 months ago

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

- 2 years, 11 months ago