JOMO 7, Short 4

Trevor creates a infinite sequence S\mathrm{S} of integers by repeatedly adding the digits 2,0,12,0,1 and 33 to the end of the previous number. For example, the first few numbers he creates are 2,20,201,2013,20132,201320,20132012, 20, 201, 2013, 20132, 201320, 2013201 \ldots

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

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