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.

## Comments

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TopNewestThanks for the mention. :D – Finn Hulse · 2 years ago

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@Jake Lai Sorry for the mistake. I have edited that problem. I could not reply there I think there is some bug. :) – Rajdeep Dhingra · 1 year, 11 months ago

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By "upper bound of a lower bound", do you mean the "greatest lower bound"? – Calvin Lin Staff · 2 years ago

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– Jake Lai · 2 years 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.Log in to reply

Cheers for the inspiration, @Finn Hulse. Hope you find this fun. – Jake Lai · 2 years ago

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