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26 Sep 2019, 05:31
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To check whether a number N is prime, adopt the following process.
(a) Take the square root of the number.
(b) Round of the square root to the immediately lower integer. Call this number Z.
For example if you have to check for 181, its square root will be 13. Hence, the value of Z, in this case will be 13.
(c) Check for divisibility of the number N by all prime numbers below z. If there is no prime number below the value of z which divides N then the number N will be prime.
To illustrate :-
The value of \sqrt{239} lies between 15 to 16. Hence, take the value of z as 15.
Prime numbers less than 15 are 2, 3, 5, 7, 11 and 13.
239 is not divisible by any of these.
Hence you can conclude that 239 is a prime number.
P.S. in order to check the divisibility, you should learn Divisibility Rules which are easy and simple, and will take far less time.
(a) Take the square root of the number.
(b) Round of the square root to the immediately lower integer. Call this number Z.
For example if you have to check for 181, its square root will be 13. Hence, the value of Z, in this case will be 13.
(c) Check for divisibility of the number N by all prime numbers below z. If there is no prime number below the value of z which divides N then the number N will be prime.
To illustrate :-
The value of \sqrt{239} lies between 15 to 16. Hence, take the value of z as 15.
Prime numbers less than 15 are 2, 3, 5, 7, 11 and 13.
239 is not divisible by any of these.
Hence you can conclude that 239 is a prime number.
P.S. in order to check the divisibility, you should learn Divisibility Rules which are easy and simple, and will take far less time.
Archit3110
26 Sep 2019, 06:44
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Aadi01
well you can use following formula to determine validity of prime
for any prime no>3 it can expressed as p=6n+1 or p=6n-1 ; n is the +ve integer value
hope this helps
well you can use following formula to determine validity of prime
for any prime no>3 it can expressed as p=6n+1 or p=6n-1 ; n is the +ve integer value
hope this helps
Aadi01
27 Sep 2019, 20:37
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Archit3110
That is correct, but remember
Prime number will be of the type 6k+1 or 6k-1, but vice versa is not true..
So, if a number>3 can NOT be written in the form 6k+1 or 6k-1, it will NOT be a prime number..
But if a number>3 is in the form 6k+1 or 6k-1, it CAN be a prime number, so you will have to check further to ascertain if that number is a prime number.
If the choices contain ONLY one in that form, you can blindly mark that answer. However, do check all the choices for this form.
