The reason why this number is associated with all the things satanic is mysterious and debatable.
Here is what is evil about the number 666!
..the number of the beast is a term. The number is 666.
The Book says it is the number of man.
"The weight of gold that came to Solomon in one year was six hundred sixty-six talents of gold."
...666 i.e. the triple representation of this number means this beast represents a government based on human authority as opposed to God's authority.
Nobody really knows what the exact meaning of this number is!