A function g(n), where n is an integer, is defined as the product of

Hello Dillesh4096

I know this are called co-primes and thats why they are not primes but, what happen if for example we have:

5! + 7 = 127 which is prime

How can we know if a number is prime or not, 5! is easy cuz we know thevalue but with bigger numbers?

Kind regards!

Hi jfranciscocuencag

In my opinion, GMAT would not ask questions like say g(6) + 7 which is 727. As finding the Prime nature of that number will be extremely difficult without any method.
But yes, i would expect them to ask the number you gave g(5) + 7 = 127.

However there is method to find whether a given number is prime or not

How to find a given number N is prime or not ?

Step 1: Find the nearest integral square root of N
Step 2: List all the prime numbers less than or equal to \(\sqrt{N}\)
Step 3: Find whether the given number N divides any of the numbers from step 2.

Conclusion: 1) If any number divides N, then N is NOT A PRIME Number
2) If no number divides N, then N is A PRIME Number

Eg1: Find whether 197 is prime or not ?

Step 1: \(\sqrt{197}\) --> Nearest integral square root = 14
Step 2: Prime numbers less than or equal to 14 --> 2, 3, 5, 7, 11, 13
Step 3: Divisibility: 2 - NO, 3 - NO, 5 - NO, 7 - NO, 11 - NO, 13 - NO.

Conclusion: 197 is A PRIME Number

Eg2: Find whether 459 is prime or not ?

Step 1: \(\sqrt{459}\) --> Nearest integral square root = 21
Step 2: Prime numbers less than or equal to 21 --> 2, 3, 5, 7, 11, 13, 17, 19
Step 3: Divisibility: 2 - NO, 3 - YES, 5 - NO, 7 - NO, 11 - NO, 13 - NO, 17 - YES, 19 - NO

Conclusion: 459 is NOT A PRIME Number

Though the above method would take around 2-2:30 minutes to solve. It's very unlikely that GMAT would test for such high numbers

Hope it's clear!