Four prime numbers in ascending order have a product of 385 for the first three and 1001 for the last three. Find the fourth number.
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Answer: A. 5
Explanation
Prime factorization of three eighty five reveals the first three prime numbers as five, seven, and eleven. Prime factorization of one thousand one yields seven, eleven, and thirteen as the last three primes. Arranging the identified prime numbers in ascending order establishes five as the initial fourth number. Prime numbers are integers greater than one that cannot be formed by multiplying smaller integers. The fundamental theorem of arithmetic states that every integer greater than one is a prime number. Factorization breaks down a composite number into the product of its constituent prime divisors.
Prime factorization is critical in modern cryptography algorithms like RSA encryption for data security. Number theory research relies heavily on understanding the distribution and properties of prime numbers. Mathematical puzzles frequently use prime products to test logical deduction and factorization skills. Option B suggests seven which represents the second number in the ascending prime sequence. Option C proposes eleven which corresponds to the middle overlap value in the prime products. Option D offers thirteen which is the final prime number in the sequence rather than the fourth.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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