It is Big enough

From the following congruences, $10^{1}=3mod7,10^{2}=2mod7,10^{6}=1mod7$ , the problem can be simplified by finding the remainder of the exponent of $10$ when divided by 6. Notice too that $10^{n}=4mod6$ for $n>1$ . Therefore the exponent of $10$ has a remainder of 4 when divided by 6. So the problem is equivalent to $(10^{4}+23)mod7$ . Thus the answer is 6.