If known, this would allow the easy generation of arbitrarily large prime numbers, which would win you some cash prizes.
It might seem like that based on the definition, but read the whole article and you'll find it's the other way around.
Mill's number is shown to exist be showing that primes in certain ranges exist, and then building the number (somewhat like constructing a number from its decimal expansion).
So you don't use Mill's number to construct prime numbers, you use prime numbers to construct Mill's number.
The EFF Cooperative Computing Award rules, by the way, specifically say that you can't just claim (say) A^(3^16) or A^(3^17) without knowing how to find their decimal expansion.
So the possibility that someone would try to use this to claim the awards with no calculate occurred to someone (maybe Landon Noll) back around 1999.
Prime numbers aren't hard to generate; just generate a bunch of random numbers and test them quickly.
For sufficiently large values of 'large', large primes are hard to generate. If (that's a big if) we had an efficient method to compute this number to arbitrary precision, we could compute primes of a billion or more bits.
Is there any point to generating primes that large? I thought one of the reasons to prefer ECC was because it uses a much smaller key than RSA.
A) A publication.
B) Eternal fame.
C) Money. See https://www.eff.org/awards/coop
And, most importantly, it may advance mathematics.
Maybe in applied math. In pure math that question would immediately reveal you as an outsider.
Yeah, it would go something like
"What are the applications of this?"
everyone gasps, stares at you
"...to the K-theory of arithmetic cobordisms."
everything goes back to normal, speaker answers the question
I remember a grad student friend in my college days telling me that when mathematicians present their work, most of their peers never understand it and this is always the safe question to ask!