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Mersenne non-prime

Source: 2021 Fall AMC10B P8/AMC10B P6

November 17, 2021
AMCAMC 10AMC 10 BAMC 12AMC 12 B

Problem Statement

The largest prime factor of 1638416384 is 22, because 16384=21416384 = 2^{14}. What is the sum of the digits of the largest prime factor of 1638316383?
<spanclass=′latex−bold′>(A)</span>3<spanclass=′latex−bold′>(B)</span>7<spanclass=′latex−bold′>(C)</span>10<spanclass=′latex−bold′>(D)</span>16<spanclass=′latex−bold′>(E)</span>22<span class='latex-bold'>(A) </span>3\qquad<span class='latex-bold'>(B) </span>7\qquad<span class='latex-bold'>(C) </span>10\qquad<span class='latex-bold'>(D) </span>16\qquad<span class='latex-bold'>(E) </span>22
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