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cakesmckakes
Lv 4
cakesmckakes asked in Science & MathematicsMathematics · 9 years ago

Using li(x) to approximate the number of prime numbers.?

Use the "logarithmic integral function, or li(x)" to approximate the number of primes less than 10^6.

I know that li(x)=integral(dt/ln(t)), t=0 to t=x, but I don't know how to use it to approximate the number of primes.

Update:

How do you approximate li(x)? I have yet to find a Taylor series expansion for it anywhere.

2 Answers

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  • Unknown
    Lv 5
    9 years ago
    Favorite Answer

    Ii(x) ~ total number of primes below x.

    So Ii(1,000,000) is the approx number of primes below 1,000,000

    For your additional query, I refer you to below:

    See this Wikepedia article the Taylor series seems and advanced and utilizes the euler constant

    http://en.wikipedia.org/wiki/Logarithmic_integral_...

  • ?
    Lv 4
    9 years ago

    Hey, since you are the first person I know to know this, wanna know something hipster I found out.

    Graph pi(x)

    Graph x/log base pi of x

    For the first 100 they are the same

    First thousand almost the same

    First ten thousand practically the same

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