[Maths Class Notes] on Is 1 a Prime Number Pdf for Exam

1 is a very unique number. In classical theory it is neither considered even, odd or anything. It is just considered as a building block for any other number. 1 is so unique that it can not be included in any group nor in the group of prime numbers. It has been seen in the ancient time there was some ambiguity regarding inclusion of 1 in the set of prime numbers. Even the great mathematician G.H.Hardy seems to be in little confusion as he included 1 in the set of prime numbers in the first six editions of his book “A Course in Pure Mathematics” till 1933. But in 1938 he updated the inclusion and considered 2 to be the first prime number to start with.

Prime Number

Before knowing if 1 is a prime number or not, let us understand what is a prime number. A prime number may be an integer greater than 1 whose only factors are 1 and itself. An element may be an integer which will be divided evenly into another number. The few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and so on. Numbers that have more than two factors are called composite numbers. The number 1 is neither prime nor composite.

For every prime p, there exists a major number p’ such p’ is bigger than p. This proof, which was demonstrated in the past by the Greek mathematician Euclid, validates the concept that there’s no “largest” prime. As the set of natural numbers N = {1, 2, 3, …} proceeds, prime numbers are generally subsided frequently and are harder to seek out in a reasonable amount of time. As of this writing, the most important known prime has 24,862,048 digits. It was discovered in 2018 by Patrick Laroche of the good Internet Mersenne Prime Search (GIMPS).

Properties of Prime Numbers

• Every number that’s greater than 1 is often divided by a minimum of one prime.

• Every even positive integer greater than the amount 2 is often expressed because of the sum of two primes.

List of Prime Numbers

Is 1 a Prime Number?

Number 1 has positive divisors for 1 and itself. consistent with the definition of a  prime number. Any number having only two positive divisors is referred to as prime numbers. So, is 1 a prime number or not? Is 1 a prime or composite number?

The answer to the present question is: No, 1 isn’t a major prime number and it’s not a composite number!

Lesson Summary:

Why is 1 not a Prime Number?

The answer to Why 1 is not a Prime Number is present in the definition for the prime numbers itself. For a number to be called the prime number, it must have only two of the positive factors. Now, for 1, the number of positive divisors or factors is only one that is 1 itself. So, this is why 1 is not a prime number here. But it is the most important number in Mathematics as it is the basic number used for forming other numbers.

 

Note: 2 is the smallest number that satisfies the definition for the prime numbers.

Solved Examples

Question 1: Which one of the following is a prime number?

Answer: 13 is a prime number because 13 has only two factors that are 13 and 1.

Question 2: Which one of the following is a prime number?

Answer: 3 is a prime number because 3 has only two factors that are 3 and 1.

Question 3: Which one of the following is a prime number?

Answer: 43 is a prime number because 43 has only two factors that are 43 and 1.

Question 4: Which one of the following is a prime number?

Answer: 53 is a prime number because 53 has only two factors that are 53 and 1.