Rem1: "or" is inclusive i.e. and/or. Rem2: number 1 is neither prime nor composite, so it does not appear on the initial list.
blackjack
<a href="http://c.casalemedia.com/c?s=51816&f=3&id=0" target="_blank"><img src="http://as.casalemedia.com/s?s=51816&u=http://perplexus.info&f=3&id=0&if=0" width="120" height="600" border="0"></a>
flooble's webmaster puzzle
