#2**+1 **

1_2 + 10_2 + 100_2 + 1000_2 +10000_2 +100000_2 + 1000000_2 + 10000000_2 + 100000000_2=?

=111111111_2 . Count the number of 1s from right to left and you get 9 "1s", from 0 to 8 as powers of 2 as follows. Start from left to right:

2^8 + 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0 =

256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 =511 in base 10. And since:

511 = 7 * 73. As you can see, the largest prime that will divide 511 is** 73.**

Guest Apr 7, 2018