It's a bit more subtle than that -- most n>2^32 are not prime in which case 2 x n has more factorizations you would have to check.
reply(Just by way of example, for n=2^33, 2n=2^34 but also =2^17*2^17)
(Just by way of example, for n=2^33, 2n=2^34 but also =2^17*2^17)