#prime counting function

[sqrt-73]

Interesting math fact of the day #144:

We know that there are 1,520,698,109,714,272,166,094,258,063 primes less than 10^29.

[still-searching-for-et]

Who says you can’t do complex analysis in Excel...

Prime Counting function using the first 200 non trivial zeroes of the Zeta function (and first 5 trivial ones).  Equation used is the main sum in the top with an approximation if you want a simpler expression to try.

Main point of the famous paper by Riemann is using the zeta zeroes you can calculate the number of primes below a number, they are one in the same, interwoven in math.

The zeroes can be found easiest using the Riemann Siegel functions lower graph (also just using excel).