MathDB

Let

A_{11}

denote the answer to problem

11

. Determine the smallest prime

p

such that the arithmetic sequence

p,p+A_{11},p+2A_{11},\cdots

begins with the largest number of primes.
There is just one triple of possible

(A_{10},A_{11},A_{12})

of answers to these three problems. Your team will receive credit only for answers matching these. (So, for example, submitting a wrong answer for problem

11

will not alter the correctness of your answer to problem

12

Problem Statement