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3. Let n be an integer greater than 2. Explain why n! +2, n! +3, n! +4, n! + (n – 1), n! +n are all composite numbers. Use this idea to obtain a list of ten consecutive composite integers.

3. Let n be an integer greater than 2. Explain why n! +2, n! +3, n! +4, n! + (n – 1), n! +n are all composite numbers. Use this idea to obtain a list of ten consecutive composite integers.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Explain why please Problem 3
y plographic methods. EXERCISESa 1. Use the sieve of Eratosthenes to find all of the primes from 100 to 200 2. Use the prime table or a computer algebra system to find a list of 31 consecutive composite numbers. 3. Let n be an integer greater than 2. Explain why n! +2, n! +3, n! +4, n! + (n – 1), n! +n are all composite numbers. Use this idea to obtain a list of ten consecutive composite integers. 4. A pair of prime numbers is called a twin prime pair if the numbers differ by 2. Find all of the twin prime pairs in the table of primes. Based on your findings, state which of the following you think is true: (1) There are infinitely many twin prime pairs. (2) There are finitely many twin prime pairs.5 Then give the product to a find the
Transcribed Image Text:y plographic methods. EXERCISESa 1. Use the sieve of Eratosthenes to find all of the primes from 100 to 200 2. Use the prime table or a computer algebra system to find a list of 31 consecutive composite numbers. 3. Let n be an integer greater than 2. Explain why n! +2, n! +3, n! +4, n! + (n – 1), n! +n are all composite numbers. Use this idea to obtain a list of ten consecutive composite integers. 4. A pair of prime numbers is called a twin prime pair if the numbers differ by 2. Find all of the twin prime pairs in the table of primes. Based on your findings, state which of the following you think is true: (1) There are infinitely many twin prime pairs. (2) There are finitely many twin prime pairs.5 Then give the product to a find the
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