They are talking about the Great Internet Mersenne Prime Search, and they can't even say
"2^n-1" out loud, but they can say
" The number is currently the world's largest prime. But there's always a larger one to find."
WOW! This sounds like a huge contradiction even if the "world's largest prime" is different from "the largest prime". Also, wouldn't it seem relevant to mention that no one has proven that there infinitely many Mersenne Primes?
Still, the part about the Hope Diamond is kind of interesting -- Are Mersenne Primes mathematical diamonds? What are your mathematical "diamonds"?
Compare with Look Around You -- Maths (the section about the longest number)