xthexder

A few calculations:

• There are 9592 prime numbers less than 100,000. Assuming the test suite only tests numbers 1-99999, the accuracy should actually be only 90.408%, not 95.121%
• The 1 trillionth prime number is 29,996,224,275,833. This would mean even the first 29 trillion primes would only get you to 96.667% accuracy.
• The density of primes can be approximated using the Prime Number Theorem: 1/ln(x). Solving 99.9995 = 100 - 100 / ln(x) for x gives e^200000 or 7.88 × 10^86858. In other words, the universe will end before any current computer could check that many numbers.

We got nerd sniped at almost the exact same time, but approached this in very different ways. I applaud your practical approach, but based on what I calculated, you should stop now. It will never reach 99.999%

99.5% would still be e^200 numbers checked (7x10^86). According to the Quora link in my other comment, we've only calculated primes in sequence up to 4x10^18 as of 7 years ago. 95% is very doable though.

Edited to correct first N primes vs primes up to N.

To be fair, I used to work there, and not even Microsoft understands their docs.