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sequence of primes build recursively

Source: Tuymaada 2002

December 6, 2006
limitnumber theory proposednumber theory

Problem Statement

A positive integer cc is given. The sequence {pk}\{p_{k}\} is constructed by the following rule: p1p_{1} is arbitrary prime and for k≥1k\geq 1 the number pk+1p_{k+1} is any prime divisor of pk+cp_{k}+c not present among the numbers p1p_{1}, p2p_{2}, …\dots, pkp_{k}. Prove that the sequence {pk}\{p_{k}\} cannot be infinite.
Proposed by A. Golovanov
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