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finite primes of form a_1 + k; a_2 + k; a_3 + k,..

Source: 12th or 13th QEDMO problem 9 (11. - 15. 12. 2013) https://artofproblemsolving.com/community/c2400093_2013_qedmo_13th_or_12th

July 5, 2021
number theoryprimes

Problem Statement

Are there infinitely many different natural numbers a1,a2,a3,...a_1,a_2, a_3,... so that for every integer kk only finitely many of the numbers a1+ka_1 + k,a2+ka_2 + k,a3+ka_3 + k,...... are numbers prime?
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