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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

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.

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

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

lmtuan
10-23-2004, 09:05 AM