In the celebrated article, "Modular Elliptic Curves and Fermat's Last Theorem", published in the Annals of Mathematics 142 (1995), 443-551, Andrew Wiles allegedly proved Fermat's Last Theorem that states that there do not exist strictly positive integers a,b,c and an integer n > 2 such that an+bn=cn. This first attempt turned out to have a serious gap that was allegedly filled by a follow-up paper, also published in the same journal, and co-authored with Richard Taylor. It turns out that even this latter "fix" must be flawed, since we found an explicit counterexample, that unfortunately is too large to be stored in any one computer. Even the storing of a,b,c, and n each requires several computers, and can only be described using holographic images (i.e. by using the Chinese Remainder Theorem). In this article, we describe the novel algorithm that lead to this counterexample (of course, an exhaustive search would be unfeasible), and give instructions for anyone who wishes to independently verify it. Due to the enormous size, it is unlikely that anyone would have the resources for a complete verification, but by taking randomly chosen primes, and once again using the Chinese Remainder Theorem, it could be verified with probability 1- ε for any desired ε > 0.