What is a Prime Number?
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?
13
6
10
4
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?
3
16
20
15
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?
12
43
90
15
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?
21
63
53
15
Answer: 53 is a prime number because 53 has only two factors that are 53 and 1.
FAQs on Is 1 a Prime Number
1. What is the theory behind not including 1 as a prime number?
In ancient mathematics there seems to be little confusion about the
inclusion of 1 as a prime number. However finally in 1938 1 was confirmed to be a prime number. The reason behind this is the uniqueness of 1. Prime number is actually a whole number which is exactly divisible by 1 and itself. This holds true for 1 but the ambiguity is that 1 and itself are not different. All other prime numbers have two different factors as the number itself and 1 but 1 has no distinct two factors. Similarly 1 can not be written as a product of the number itself and 1 since in that case 1 will lose its uniqueness thus there is a solid reason for not considering 1 as a prime number.
2. How to find whether the given number is prime or not?
There are certain simple methods to find whether the given number
is prime or not. They are as follows:
Determine all the factors of the given number
If the total number of factors is only two i.e 1 and the number itself then it is a prime number.
For large numbers if it ends with 0,2,4,6,8 then the number is not a prime number since there will be more than two factors of the number. One of them is sure to be 2. So at least three factors or maybe more are there.
If the sum of all the digits of the large number has a factor of 3 then it cannot be a prime number.
If the square root of the number has prime numbers then divide the number itself by those prime numbers and that gives a number less than the square root value then the actual parent number is not a prime number.
3. Which numbers are called co-prime numbers?
Co-prime numbers are the numbers which themselves may or may not be prime
numbers but there will be only one common factor between the numbers and that
will be 1 only. Co prime numbers have to be a minimum of two numbers at a time.
More than two numbers can be referred to as co prime numbers if they have only
one common factor of 1 between them. For example 1,2, 7 which have only 1 as a
A common factor between them can be referred to as co-prime numbers.
4. Why is it important to know about the prime numbers?
Knowledge of prime numbers is important in real life. They are basically the skeletal frame or the building blocks of all the whole numbers. It is of great importance for communication. In modern days prime factors of large numbers are used in computer cryptography. We have heard a lot about encryption while using our social media in the form of Whatsapp or other modes of social communication. This encryption solely lies on the usage of prime numbers.Prime numbers are widely used in determining the colour intensity in pixels which we always search for in our camera.
5. What type of number is 1?
One is neither an odd number or a composite number based on the theory of the number of factors it has. It is not a prime number because although it has two factors of 1 and itself, they are the same and one. 1 is also not a composite number since it has only one positive factor of 1 but composite numbers are those which have more than two positive factors. Then what is 1. It is an unique building block which can be included under the head of either of the following groups.
Natural number
Odd number
Rational number
Positive integer
Whole number