Saturday, May 2, 2020

Prime numbers

Prime numbers are the numbers with two factors, 1 and the number itself. For example, 7 is a prime number, which is divisible by 1 and 7 only. If we divide 7 with any other number then a fraction value is produced. The contradictory part of a prime number is a composite number, which has more than two factors. In the number system, we have learned many types of numbers out of which prime and composite numbers are the most significant ones.


What is a Prime Number?

A prime number is a positive integer having exactly two factors. If p is a prime, then it’s only factors are necessarily 1 and p itself. Any number which does not follow this is termed as composite numbers which means that they can be factored into other positive integers.
First Ten Prime Numbers
The first ten primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
Note: It should be noted that 1 is a non-prime number.

List of Prime Numbers 1 to 100


As we know, the prime numbers are the numbers which have only two factors which are 1 and the numeral itself. There are a number of primes in the number system. Let us provide here the list of prime numbers that are present in 1 to 100 numbers along with their factors and prime factorisation.
Prime Numbers from 1 to 100FactorsPrime Factorisation
21, 21 x 2
31, 31 x 3
51,5 1 x 5
1,7 1 x 7
111,11 1 x 11
131, 131 x 13
171, 171 x 17
191, 191 x 19
231, 231 x 23
291, 291 x 29
311, 311 x 31
371, 371 x 37
411, 411 x 37
431, 431 x 43
471, 471 x 47
531, 53 1 x 53
591, 59 1 x 59
611, 61 1 x 61
671, 671 x 67
711, 71 1 x 71
731, 73 1 x 73
791, 79 1 x 79
831, 831 x 83
891, 891 x 89
971, 97 1 x 97

Prime Numbers Chart


The chart below shows the list of prime numbers, which are represented in the coloured box.



Properties of Prime Numbers

Some of the properties of prime numbers are:
  • Every number greater than 1 can be divided by at least one prime number.
  • Every even positive integer greater than 2 can be expressed as the sum of two primes.
  • Except 2, all other prime numbers are odd. In other words, we can say that 2 is the only even prime number.

Each composite number can be factored into prime factors, and individually all of these are unique in nature.

Difference Between Prime Numbers and Composite Numbers

Prime NumbersComposite Numbers
A prime number has two factors only.A composite number has more than two factors.
It can be divided by 1 and the number itself.
For example, 2 is divisible by 1 and 2.
It can be divided by all its factors. For example, 6 is divisible by 2,3 and 6.
Examples: 2,3,7,11,109, 113,181, 191,etc.Examples: 4,8,10,15,85,114,184, etc.

Is 1 a Prime Number?

Conferring to the definition of the prime number which states that a number should have exactly two factors for it to be considered a prime number. But, number 1 has one and only one factor which is 1 itself. Thus, 1 is not considered a Prime number.
Examples: 2,3,5,7,11 etc
In all the positive integers given above, all are either divisible by 1 or itself i.e exactly two positive integers.

Smallest Prime Number

The smallest prime number as defined by modern mathematicians is 2. To be prime, a number must be divisible only by 1 and the number itself which is fulfilled by the number 2.

Largest Prime Number

As of January 2016, the largest known prime number is 2{77,232,917} – 1, a number with 23,249,425 digits. It was found by the Great Internet Mersenne Prime Search (GIMPS).

Prime Numbers Examples

Example 1:
Is 10 a Prime Number?
Solution:
No, because it can be divided evenly by 2 or 5, 2×5=10, as well as by 1 and 10.
Example 2:
Is 19 a Prime Number?
Solution:
Let us write the given number in the form of 6n ± 1.
6(3) + 1 = 18 + 1 = 19
Therefore, 19 is a prime number.
Example 3:
Find if 53 is a prime number or not?
Solution:
The only factors of 53 are 1 and 53.
So, 53 is a prime number.
Example 4:
Check if 64 is a prime number or not?
Solution:
The factors of 64 are 1, 2, 4, 8, 16, 32, 64.
Hence it is a composite number and not a prime number.






How to Find Prime Numbers?

To find whether a number is prime, try dividing it with the prime numbers 2, 3, 5, 7 and 11. If the number is exactly divisible by any of these numbers, it is not a prime number, otherwise, it is a prime.

Can Prime Numbers be Negative?

No, a prime number cannot be negative. According to its definition, a prime number is a number greater than 1 which is only divided by itself and 1.

Which is the Largest Known Prime Number?

The number M77232917 is the largest prime number having 23,249,425 digits.






What is the Difference Between a Prime and a co-prime Number?

A prime number is a number which is divisible by 1 and itself while a co-prime number is a number which does not have any common factor between them other than 1. It should be noted that 2 prime numbers are always co-prime.

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