A counterexample to the prime conjecture of expressing numbers using just ones

TextLet f(n)f(n) be the least number of ones that can be used to represent n using ones and any number of + and × signs (and parentheses). It is always true that for a prime p  , f(p)=f(p−1)+1?f(p)=f(p−1)+1? Itʼs in the famous book Unsolved Problems in Number Theory   as problem F26 written by R.K. Guy. The aim of our work is to give a counterexample to the conjecture and some properties on f(n)f(n).VideoFor a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=R8IQI_dwaJE.