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How many primes are there in a certain range of numbers?

by newcool
Tags: numbers, primes, range
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newcool
#1
Jan19-05, 07:26 PM
P: 42
Hi, what would be the best estimate in the # of primes between [tex]10^{100}[/tex] and [tex]10^{101} [/tex]

thanks
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kreil
#2
Jan19-05, 08:00 PM
kreil's Avatar
P: 546
I'm not sure if there is a newer equation, there probably is one from riemman, but Gauss had a formula for approximating the number of primes up to any number x:

[tex]Li(x)=\int_0^x\frac{dt}{log(t)}[/tex]

You could compute this for 10100 and then for 10101 and subtract the first result from the second and it will give a good estimate.


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