P vs NP is also distinguished in that many people think it has profound philosophical implications. Nick Land seems to think this (http://www.uf-blog.net/crypto-current-021/), and so does Scott Aaronson (“if P=NP, the word would be a profoundly different place than we usually assume it to be ... there would be no value in “creative gaps””). Though I think Land’s idea is a lot more interesting — he says P vs NP is a paraphrase of the analytic vs synthetic distinction.