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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, 2 months ago

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Thanks for the mention. :D Finn Hulse · 2 years, 2 months 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 · 2 years, 1 month ago

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

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@Calvin Lin 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 · 2 years, 2 months ago

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

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