for any n belong to the set of natural number defind Pn as the set of all prime number that are the sum of n consecutive prime numper that is

Pn=a set of Pk belong to prime number P, such that Pk={ sum of i from 1 to n where Pr+i-1,Pr+i-1 and so on belong to prime number P ,r belong to the set of natural number} frist prove that p1=P second find p2 and p4 explain why these are finit sets,hence, prove whether the same applies for every even value of n. third find the five element in each of sets p3 and ,p5 explian where these shoud be finit or infinit sets?
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