JOMO 7, Short 4

Trevor creates a infinite sequence \(\mathrm{S}\) of integers by repeatedly adding the digits \(2,0,1\) and \(3\) to the end of the previous number. For example, the first few numbers he creates are \(2, 20, 201, 2013, 20132, 201320, 2013201 \ldots\)

Find the number of primes in \(\mathrm{S}\).

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