X=(2^58+1)/5
if X is divisible by 5 then last digit must end with 0,5
for this 2^58 must end with 4 or 9,9 not possible
2^2=4
2^6=64
2^10=1024
2^14=16384
......
So got the catch,removing first 2 from 58 we are left with 56 & it
is divisible by 4,so we conclude X IS AN INTEGER.
Now catch this pattern
(2^6+1)/5=13(prime)
(2^14+1)/5=(prime)
(2^22+1)/5=(prime)
(2^30+1)/5=(prime)
......
leaving 2 we have 56 & it is also divisible by 8,but our pattern passes through 54 not through 58 so we conclude X IS NOT A PRIME

Posted by Nishant
on 20070410 15:52:41 