Question

Prove or disprove the following statements by giving justification: (4.5)

a. The sum of two prime numbers is always prime number.

b. The product of two prime numbers is also a prime number.

c. There exist exactly four prime numbers between 100 and 150​

Answer 1

Answer:

Step-by-step explanation:

a. The sum of two prime numbers is always prime number.

Let the the prime numbers are p1 and p2

Case I

p1=2,p2=5

p1+p2=2+5=7 ( prime)

case II

p1=2,p2=7

p1+p2=2+7=9 ( no prime)

case III

p1=5, p2=23

p1+p2=5+23=28 ( non prime)

b. The product of two prime numbers is also a prime number.

Product =p1 * p2( product of two number)

This is a composite so it is a non prime number

Disproved

c. There exist exactly four prime numbers between 100 and 150​

Prime numbers between 100 and 150

101,103,107,109,113,127,131,137,139,149 ( 10 No)

Disproved