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Adding a to each integer in the sequence gives a prime

Source: Baltic Way 1999

December 23, 2010
number theory proposednumber theory

Problem Statement

Does there exist a finite sequence of integers c1,c2,…,cnc_1,c_2,\ldots ,c_n such that all the numbers a+c1,a+c2,…,a+cna+c_1,a+c_2,\ldots ,a+c_n are primes for more than one but not infinitely many different integers aa?
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