well...

Binary numbers always follow the pattern 2, 4, 8, 6 in the final digit...

so 2014 mod 4=2... so we know that 2^2014 ends in 4.

and 7 * 7 * 7 * 7 ends in 1.

So we know that this number ends in 5, and thus is not prime.

well...

Binary numbers always follow the pattern 2, 4, 8, 6 in the final digit...

so 2014 mod 4=2... so we know that 2^2014 ends in 4.

and 7 * 7 * 7 * 7 ends in 1.

So we know that this number ends in 5, and thus is not prime.

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