Riemann Zeta Function and Prime Numbers

This last example is rather difficult but will really sharpen your mathematical wits if you can master it (do not worry if you cannot). 

The function is finite for all values of in the complex plane except for the point = 1. Euler in 1737 proved a remarkable connection between the zeta function and an infinite product containing the prime numbers  

The product notation n is analogous to E for sums. More explicitly. 

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