Finding prime numbers which are generated by other primes

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  1. Find the prime(s) generated by the alternate primes 2,5,11,17.

  2. Find the prime(s) generated by the first five primes 2,3,5,7,11.

We are allowed to use all arithmetic operators.

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  1. Your task is to find the prime factors of $2\cdot 5\cdot 11\cdot 17+1$, that are not among $2,5,11,17$.

  2. Your task is to find the prime factors of $2\cdot 3\cdot 5\cdot 7\cdot 11+1$, that are not among $2,3,5,7,11$.