Four prime numbers in ascending order have a product of 7429 for the first three and 12673 for the last three. Find the fourth number.
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Answer: B. 29
Explanation
Prime factorization of seven thousand four29 yields the product of the first three consecutive prime numbers as seventeen, nineteen, and twenty-three. Prime factorization of twelve thousand six hundred seventy-three yields the product of the last three primes as nineteen, twenty-three, and twenty-nine. Comparing the overlapping prime sequences identifies the fourth and final prime number in ascending order as twenty-nine. Prime numbers are integers greater than one that can only be divided evenly by one and themselves. Fundamental theorem of arithmetic states that every integer greater than one is either a prime number itself or can be represented as a unique product of primes. Sequential prime analysis requires breaking large composite products down into their irreducible foundational components.
Option A represents seventeen, which is the first number in the sequence rather than the fourth number. Option C represents twenty-three, which is part of both overlapping groups but not the final fourth number. Option D is incorrect if chosen as a distractor, though twenty-nine is actually the correct fourth number identified in the explanation.
- Subject
- Mathematics
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- Mathematics
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