Bitcoins are growing rapidly and are becoming more common. At present there are some countries that accept bitcoin and allow people to be used to purchase or pay bills. So I think bitcoin can last more than 100 years.
As of now bitcoin is the best cryptocurrency when compared to other and can rate it as no.1, but can't predict for the next 100yers, who knows what happens in the next 100 years, but with the positive note can think and predict that it may stay for 100 years, unless another type of currency exists.
It will be surviving for more than 100 years if any major crash doesn't happen in cryptocurrency market. There is no reason preventing bitcoin from living after the year, 2100.