# Seemingly Difficult but too easy!!!

Number Theory Level 2

Trevor creates an infinite sequence $$S$$ of integers by repeatedly adding the digits $$2,0,1$$ and $$3$$ to the previous numbers in the sequence. For example, the first few numbers that he forms are: $$2,20,201,2013,20132,201320,2013201,20132013,201320132$$ and so on. Find the number of primes in $$S$$.

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