verdant

10-21-2004, 05:59 AM

If n is any prime number greater than 2, which of the following CANNOT be a prime number?

n-4

n-3

n-1

n+2

n+5

n-4

n-3

n-1

n+2

n+5

View Full Version : please look at this one 3

verdant

10-21-2004, 05:59 AM

If n is any prime number greater than 2, which of the following CANNOT be a prime number?

n-4

n-3

n-1

n+2

n+5

n-4

n-3

n-1

n+2

n+5

gre_nidhi

10-21-2004, 06:33 AM

is it n+5..

if yes then i just did by ellimaination so would like somebody to explain it.

if yes then i just did by ellimaination so would like somebody to explain it.

cskumar

10-21-2004, 06:52 AM

See, All primes greater than 2 are odd;

So, n-4 is odd and can be prime but take n=6 gives n-4=2 is prime

n-3 could be even ie prime

n-1 sameway as above is prime

n+2 is odd and can be prime as the case is in 41, 43 & 11, 13 etc

n+5 is always even for all odds greater than 2 and hence is the answer

So, n-4 is odd and can be prime but take n=6 gives n-4=2 is prime

n-3 could be even ie prime

n-1 sameway as above is prime

n+2 is odd and can be prime as the case is in 41, 43 & 11, 13 etc

n+5 is always even for all odds greater than 2 and hence is the answer

lmtuan

10-23-2004, 09:04 AM

Since all primes greater than 2 are odd, then n is an odd integer and n is greater than or equal to 3.

So,

1* n-4 is odd and can be prime.

Eg: n=7 ---> n - 4 = 3 is a prime number

n=17 ---> n - 4 = 13 is a prime number

........................

2* n-3 is even, but can be prime

Eg: n=5 ---> n - 3 = 2 is a prime number

3* n-1 is even, but can be prime

Eg: n=3 ---> n - 1 = 2 is a prime number

4* n+2 is odd and can be prime

Eg: n=3 ---> n + 2 = 5 is a prime number

n=5 ---> n + 2 = 7 is a prime number

n=11 ---> n + 2 = 13 is a prime number

..............................

5* Since n is an odd number and n>2, then (n+5) is an even number and n+5>7.

Hence, n+5 must be a composite number , it can not be a prime number

NOTE: The unique even prime number is 2

So,

1* n-4 is odd and can be prime.

Eg: n=7 ---> n - 4 = 3 is a prime number

n=17 ---> n - 4 = 13 is a prime number

........................

2* n-3 is even, but can be prime

Eg: n=5 ---> n - 3 = 2 is a prime number

3* n-1 is even, but can be prime

Eg: n=3 ---> n - 1 = 2 is a prime number

4* n+2 is odd and can be prime

Eg: n=3 ---> n + 2 = 5 is a prime number

n=5 ---> n + 2 = 7 is a prime number

n=11 ---> n + 2 = 13 is a prime number

..............................

5* Since n is an odd number and n>2, then (n+5) is an even number and n+5>7.

Hence, n+5 must be a composite number , it can not be a prime number

NOTE: The unique even prime number is 2

lmtuan

10-23-2004, 09:05 AM

THus, answer is (n+5)