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Hi, i hope u understand it with this proof:

o Let n be the pumping lemma value and let k be a prime

greater than n.

o If L is regular, the Pumping Lemma implies that a^k can be decomposed into

xyz, |y| > 0, such that xy^iz is in L for all i >= 0.

o Assume such a decomposition exists.

o The length of w = xy^k+1z must be a prime if w is in L. But

length(xyk+1z) = length(xyzyk)

= length(xyz) + length(yk)

= k + k(length(y)

= k (1 + length(y))

o The length of xy^k+1z is therefore not prime, since it is the

product of two numbers other than 1. So xy^k+1z is not in L.

o Contradiction!

You

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