In the window of my pocket calculator, I can see a six-figure number, abcdef, with distinct digits between 1 and 9. A close inspection of the digits reveals that abcdef, cdef, and def are all prime numbers.

If I turn the calculator upside-down, I see that uvwxyz and wxyz are also prime numbers.

Which number is displayed in the window of my pocket calculator and what is the upside-down version of it?

Full credit for this problem goes to Ajit Athle who has very kindly given his permission for the puzzle to be posted here.

(In reply to Solution (spoiler) by Leming)

   10   N=99999
   20   while N<999999
   30     N=nxtprm(N)
   40     Ns=cutspc(str(N))
   50     Good=1:Bkwd=""
   55     for I=1 to len(Ns)-1
   56       if instr(mid(Ns,I+1,*),mid(Ns,I))>0 then Good=0
   57     next
   60     for I=1 to len(Ns)
   70       if instr("0347",mid(Ns,I,1))>0 then Good=0
   71       C=mid(Ns,I,1):if C="6" then C="9":else if C="9" then C="6"
   75       Bkwd=C+Bkwd
   80     next
   90     P1=val(mid(Ns,3,*)):P2=val(mid(Ns,4,*))
   91     P3=val(Bkwd):if prmdiv(P3)<>P3 then Good=0
   94      P4=val(mid(Bkwd,3,*)):if prmdiv(P4)<>P4 then Good=0
  100     if Good=1 and prmdiv(P1)=P1 and prmdiv(P2)=P2 then print N;P1;P2;prmdiv(P3);prmdiv(P4):Ct=Ct+1
  200   wend

finding

158269  8269  269  692851  2851

I could have used nested ifs and premature exits from loops, but UBASIC's structure makes that not worth the bother just to get an answer in a fraction of a second rather than 2 seconds.

Posted by Charlie on 2006-12-15 11:15:45