27 is a cube number using only prime digits.

What is the other one?

I believe there is only one!
Correct me if I am wrong.

I also just found one more going to n^3 <10^18 

winner:      27  =  3 ^3

winner: 3375   = 15 ^3

 n max =               1000000

rabbit-3:~ lord$ more t40.f

        program testtt

        integer*8 i,dum,three,d,ten,n

        integer ndig,num(18)

        ten=10

        three=3

           do 2 i = 3,9999999,2

           dum=i**three

           ndig=1+log10(1.*dum)

                if(ndig.gt.18)then

                print*,'n max = ',i

                stop

                endif

           d=dum

                do n=ndig-1,0,-1

                p=ten**n

                num(n+1)=dum/ten**n

                dum = dum - num(n+1)* ten**n

                enddo

                do  k=1,ndig

                if(num(k).ne.2.and.num(k)

        1       .ne.3.and.num(k).ne.5.and.num(k).ne.7)go to 2 

                enddo

                print*,'winner: ',d,' = ',i,'^3'        

2          enddo

        end

Edited on October 24, 2018, 10:46 am

Posted by Steven Lord on 2018-10-24 10:21:41