Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
The answer is yes to both questions: it is a theorem of Brillhart, Filaseta, and Odlyzko (see corollary 2, p.1058):
http://cms.math.ca/10.4153/CJM-1981-080-0
