tag:blogger.com,1999:blog-11569812.post113143880957393984..comments2023-05-24T06:22:25.402-07:00Comments on The Orange Juice Files: Lots of primes, but not so many proofsTheohttp://www.blogger.com/profile/03344294173628793721noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-11569812.post-1131439342924985322005-11-08T00:42:00.000-08:002005-11-08T00:42:00.000-08:00I do, however, consider the following a distinct p...I do, however, consider the following a distinct proof:<BR/><I>By unique factorization, the harmonic sum \sum_{n=1}^{\infty} 1/n can be factorized as \prod_{p prime} \sum_{n=0}^\infty 1/p^n = \prod_{p prime} 1/(p-1). But the harmonic sum diverges, and so the product must be infinite.</I><BR/><BR/>I even consider this a different proof:<BR/><I>By unique factorization, the sum \sum_{n=1}^{\infty} Theohttps://www.blogger.com/profile/03344294173628793721noreply@blogger.com