Find the largest prime number (in decimal form) that divides the sum, $$ 1_2 + 10_2 + 100_2 + \cdots + 100000000_2. $$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the largest prime number (in decimal form) that divides the sum, $$ 1_2 + 10_2 + 100_2 + \cdots + 100000000_2. $$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
73
Find the largest prime number (in decimal form) that divides the sum, $$ 1_2 + 10_2 + 100_2 + \cdots + 100000000_2. $$
train