User blog comment:Simplicityaboveall/The Construction of Extremely Large Numbers/@comment-24920136-20160725013617/@comment-29014792-20160725160053

No... K < e_0
 * 10^10 = w^w
 * 10^10+1 = w^w+1
 * 10^10*2 = w^w*2
 * 10^11 = w^(w+1)
 * 10^12 = w^(w+2)
 * 10^x = w^K[x]