I wrote:

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For any prime p consider the mapping f_p : N -> N given by f_p(n) = p*n + 1.

Consider (possibly finite) sequences of primes

(*)   q_0, q_1, q_2, ..., where q_(n+1) = f_p(q_n) for n = 0,1,2,...
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Another question:  If there are no infinite sequences (*) composed purely of primes, do there exist sequences (*) that *contain* infinitely many primes?  If so, how large can the density of the primes be in (*) ???

--Dan A.