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no infinte sequance of primes with p_{k+1} = 2p_k - 1 or p_{k+1} = 2p_k + 1

Source: Switzerland - 2012 Swiss MO Final Round p4

December 30, 2022
number theoryprimeprimesrecurrence relation

Problem Statement

Show that there is no infinite sequence of primes p1,p2,p3,...p_1, p_2, p_3, . . . there any for each k k: pk+1=2pk−1p_{k+1} = 2p_k - 1 or pk+1=2pk+1p_{k+1} = 2p_k + 1 is fulfilled.
Note that not the same formula for every kk.
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