Project Euler/7: Difference between revisions
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Project Euler, question 7: https://projecteuler.net/problem=7 | |||
Solution: https://git.charlesreid1.com/cs/euler/src/master/007 | |||
==The Question== | ==The Question== | ||
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<math> | <math> | ||
\dfrac{x}{ln{(x)}} = | \dfrac{x}{ln{(x)}} = 10,001 | ||
</math> | </math> | ||
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x \approx 116,000 | x \approx 116,000 | ||
</math> | </math> | ||
{{ProjectEulerFlag}} | |||
Latest revision as of 03:50, 9 October 2019
Project Euler, question 7: https://projecteuler.net/problem=7
Solution: https://git.charlesreid1.com/cs/euler/src/master/007
The Question
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
What is the 10,001st prime number?
https://projecteuler.net/problem=7
Approach
Start with the prime number distribution function pi(x),
$ \pi(x) \approx \dfrac{x}{\ln{(x)}} $
This gives us a ballpark estimate of how many numbers we will need to look at to find the 10,001st prime number: just solve
$ \dfrac{x}{ln{(x)}} = 10,001 $
or,
$ x \approx 116,000 $
