2018 AMC 10 B

Complete problem set with solutions and individual problem pages

Problem 11 Easy

Which of the following expressions is never a prime number when p is a prime number? (2018 AMC 10B Problem, Question#11)

  • A.

    p^2+16

  • B.

    p^2+24

  • C.

    p^2+26

  • D.

    p^2+46

  • E.

    p^2+96

Answer:C

Because squares of a non-multiple of 3 is always 1 mod 3, the only expression is always a multiple of 3 is \rm(C)~p^2+26. This is excluding when p=0 mod 3, which only occurs when p=3, then p^2+26=35 which is still composite.

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