Question

Q1. Define the following terms :-
(i) Co- Prime Numbers
(ii) Twin Prime Numbers
(iii) Prime Triplet

Q2. Why 1 is neither prime nor composite?

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Answer 1

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Question1.

Define the following terms:-

(i) Co- Prime:- Consecutive prime numbers[a, b] such that 'a' is prime with respect to 'b' and 'b' is prime with respect to 'a'. And there HCF is always 1.

Example:- [1,2] HCF = [a, b] = 1

⇒a, b are not compulsory to be prime.

⇒HCF(a, b) =1

(ii) Twin Prime :- Prime Number differing by 2 are called Twin-Prime.

⇒Example:-(3, 5),(11,13) etc.

⇒There are infinite twin Primes.

(iii) Prime Triplet :- Prime Triplet is a set of three prime numbers which differs by 2.

Question 2 :- Why 1 is neither prime nor composite?

⇒For being Prime Number it should have two factors and for being composite number it should have factors more than 2 factors but 1 has only one factor that it is itself so it is neither prime nor composite.

Answer 2

Answer:

Co- Prime:- Consecutive prime numbers[a, b] such that 'a' is prime with respect to 'b' and 'b' is prime with respect to 'a'. And there HCF is always

(ii) Twin Prime :- Prime Number differing by 2 are called Twin-Prime.