A number theory problem by Yash Singhal

Trevor creates an infinite sequence SS of integers by repeatedly adding the digits 2,0,12,0,1 and 33 to the previous numbers in the sequence. For example, the first few numbers that he forms are: 2,20,201,2013,20132,201320,2013201,20132013,2013201322,20,201,2013,20132,201320,2013201,20132013,201320132 and so on. Find the number of primes in SS.

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