I was trying to explain to my family last night why 1 is not generally defined as a prime number and I thought of the Zeta Function. There is the standard way to write it,(adsbygoogle = window.adsbygoogle || []).push({});

(1)[tex]\zeta(s)=\sum_{n=1}^{\infty}n^{-s}[/tex]

but then there is also the Euler product formula:

(2)[tex]\prod_{p}\frac{1}{1-p^{-s}}[/tex]

Obtaining the product formula through the sieving method requires one to factor out (1-1/p) from the (1) equation, p being prime numbers starting at 2. If we include 1 as a prime number, this entire method would fail.

Do you think this is a good way of showing why analytically 1 should not be considered prime?

Jameson

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# Zeta function justifying 1 not being prime?

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