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twin primes?

Source: 2022 AMC 10B P13

November 17, 2022
AMCAMC 102022 AMC 10B2022 AMCprimesdifference of cubes

Problem Statement

The positive difference between a pair of primes is equal to 22, and the positive difference between the cubes of the two primes is 3110631106. What is the sum of the digits of the least prime that is greater than those two primes?
<spanclass=′latex−bold′>(A)</span>8<spanclass=′latex−bold′>(B)</span>10<spanclass=′latex−bold′>(C)</span>11<spanclass=′latex−bold′>(D)</span>13<spanclass=′latex−bold′>(E)</span>16<span class='latex-bold'>(A) </span> 8 \qquad <span class='latex-bold'>(B) </span> 10 \qquad <span class='latex-bold'>(C) </span> 11 \qquad <span class='latex-bold'>(D) </span> 13 \qquad <span class='latex-bold'>(E) </span> 16
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