# Generating function for the nth prime

Is there a generating function for nth prime that is easy to deal with? i.e. is there a simple closed form for the series $p_1x + p_2x^2 + ...$ or of the form $\sum_{n = 1}^\infty x^{p_n}$

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Mayank Pandey, you are truly an optimist –  John Wiltshire-Gordon Nov 4 '13 at 18:05
The short answer is 'no'. Relevant reading material: en.wikipedia.org/wiki/Formula_for_primes Did you research this question before asking it? –  user43208 Nov 4 '13 at 18:09

## migrated from mathoverflow.netNov 4 '13 at 21:05

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How about a generating function of the form $$\left(1-p_1^{-s}\right)\left(1-p_2^{-s}\right)\left(1-p_3^{-s}\right)\cdots = \frac{1}{\zeta(s)},\qquad \mathrm{Re}\;s > 1$$