# Smallest prime factor of $\lfloor e\uparrow e\uparrow e\uparrow e\rfloor$?

What is the smallest prime factor of $$\lfloor e\uparrow e\uparrow e\uparrow e\rfloor$$ To get this number start with $1$ and apply the $\exp$-funtion four times, then take the integer part. This number is an enormous number, having $$1\ 656\ 521$$ digits (Note that this happens to be a prime number!). I was curious and, for fun wanted to determine the smallest prime factor, expecting that I will soon find a prime factor.

But it turned out that the number has no prime factor below $10^9$.

What is the smallest prime factor of the above number ? Can we do any better than trial division ?

A primilaty test will take long for such a large number and even the pollard-rho-method is slow (at least with PARI/GP). I would like to check the number with PFGW or with yafu, but I do not know how to copy such a large number such that yafu or PFGW can read it.

And maybe , this number has already been checked by someone. Who can give a link or helps to find a factor ?

• Curiosity question: Do these questions ever get answered? – Simply Beautiful Art Oct 26 '17 at 1:39