Q2: Use the definitions of prime numbers to justify your answers to the followin
ID: 3730210 • Letter: Q
Question
Q2: Use the definitions of prime numbers to justify your answers to the following questions
Definition :
An integer n is a prime if and only if, n > 1 and for all positive integers r and s, if n = rs, then either r or s equals n. An integer n is composite if and only if n > 1 and n = rs for some integers r and s with 1<r<n and 1<s<n.
In symbols:
n is prime for all positive integers r and s, if n=rs then either r =1 and s=n or r=n and s=1.
n is composite positive integers r and s such that n=rs and 1<r<n and 1<s<n.
a. Is 1 prime?
b. Is every integer greater than 1 either prime or composite?
c. Write the first six prime numbers.
d. Write the first six composite numbers.
Explanation / Answer
a) 1 is not prime since according to the definition given prime number should be greater than 1.
b) Yes , every number integer than 1 is either prime or composite because according to the definition given, n=rs composite number implies1<r<n and 1<s<n. so every number other than prime number will be obtained by multiplying two numbers which are greater than 1.
c) First six prime numbers are 2,3,5,7,11,13.
d) First 6 composite numbers are 4,6,8,9,10,12
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