Why did we choose n+1 in this proof of pumping lemma for context free language? I can't understand what are we trying to show by choosing i=n+1

[shivajikobardan]

Prime number CFG and Pumping Lemma

So I have a problem that I'm looking over for an exam that is coming up in my Theory of Computation class. I've had a lot of problems with the pumping lemma, so I was wondering if I might be able ...

cs.stackexchange.com

Even here


same thing is done, what is the reason behind choosing i= givenprimelength+1

Here is more detail.

https://www.cs.sjsu.edu/~mak/archive/CS154/assignments/5/Assignment5Solutions.pdf

 

[blamocur]

Choosing $i = n+1$ gets you a non-prime number $n+n*(j+k) = (n+1)(j+k)$. But this is the length of a "pumped" string, which, according to the lemma, must be in $L_3$ and thus have a prime length. The resulting contradiction proves that a set of all strings of prime length is not a context-free language.