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

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The discussion focuses on estimating the number of prime numbers between 10^100 and 10^101. A suggested method involves using the logarithmic integral function, Li(x), which approximates the number of primes up to a given number x. By calculating Li(10^101) and Li(10^100) and subtracting the two results, one can obtain a reliable estimate for the number of primes in that range. The mention of Riemann's work implies there may be more recent advancements in prime number estimation, but Gauss's formula remains a valid approach. This method provides a practical way to estimate primes in large numerical ranges.
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Hi, what would be the best estimate in the # of primes between 10^{100} and 10^{101}

thanks
 
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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:

Li(x)=\int_0^x\frac{dt}{log(t)}

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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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