# What does this notation mean for calculating prime?

I'm not very proficient with math, but Ive managed to make my way to problem 7 of Project Euler using python. I have to now find the 10,001st prime number. I'm reading about Eucilid's theorem. But I'm afraid I do not understand enough about mathematical notation to understand the theorem.

What do the numbers in the p=p1,p2,p3 expression on this page (http://en.wikipedia.org/wiki/Euclid%27s_theorem#Euclid.27s_proof) mean? Is p the prime number? and the 1,2,3,4 are just counting the position?

• Are you referring to the equation $P = p_1 p_2 \dotsm p_n$ in the first section? – epimorphic Jul 6 '14 at 17:08

To turn this into the language of a programmer, $p$ is essentially an array of prime numbers. So $p_1$ is the first element of the array, $p_2$ is the second, and so on.
• @ReneSchipperus Generally speaking, you are correct, there is no formula for the $n$-th prime (if you were to figure one out then you'd win every prize in mathematics). – lemon Jul 6 '14 at 16:34
• @ReneSchipperus OF course this is possible without computer. I'm pretty sure some the "old ones" listed all primes up to several millions. After all they also computed $30§ decimals of$\pi$by hand or manually divised a method to construct the regular$257\$-gon with straightedge and compasses. – Hagen von Eitzen Jul 6 '14 at 16:38