Did you ever wonder before how many prime numbers are there? Well, if you had, good for you because you will get to know the answer. If you havn't, it is also good for you as you will get to learn something new!
Firstly, if you want to find out if a number is a prime, you will have to square the number, then find out if that number is divisible be all the primes below the result.
So, in order for a number to be not prime, it will have to be divisible by at least a prime.
Also note that a number have no common factors with the number 1 lesser or more than itself.
eg. (X+1) have no common factors with ( X ).
Lets go to the extreme, when all the prime numbers are multiplied together.
Let prime be P (P1= first prime number, P2= second prime number and so on).
P1 x P2 x P3 x ........ x Pn= T
Since T cannot have any common factors with (T+1), so (T+1) is not divisible by any prime number. Hence, (T+1) is a prime number!
Therefore the conclusion is that there are infinitely numbers of primes as there are infinitely possible solutions for T!
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