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 Prime Product Permutation (Posted on 2005-03-21)
Find three different digits that no matter in what order they are arranged, the three digit number formed is the product of two primes.

 See The Solution Submitted by Old Original Oskar! Rating: 3.2500 (4 votes)

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 Exhaustive Search via computer program -- spoiler | Comment 1 of 4

100   for D1=0 to 7
200   for D2=D1+1 to 8
300   for D3=D2+1 to 9
400   Good=1
500   B\$=cutspc(str(D1))+cutspc(str(D2))+cutspc(str(D3))
600   for Ii=1 to 6
700    N=val(B\$)
800    P=2
900    T=N:Ct=0
1000    while P<=sqrt(T)
1100      if T@P=0 then
1200        :Ct=Ct+1:T=T//P
1300      :else
1400        :P=nxtprm(P)
1500    wend
1510   if T>1 then Ct=Ct+1
1600    if N>99 and Ct<>2 then Good=0:cancel for:goto *NotGood
1700    gosub *Permute(&B\$)
1800   next Ii
1900   if Good then print D1,D2,D3
2000   *NotGood
2100   next D3
2110   next D2
2120   next D1
2200   end
2300
2400   *Permute(&A\$)
2500   local I,J,X\$,Fl
2600    X\$=""
2700    for I=len(A\$) to 1 step -1
2800     L\$=X\$
2900     X\$=mid(A\$,I,1)
3000     if X\$<L\$ then cancel for:goto *Outta
3100    next I
3200   *Outta
3300    if I=0 then
3400     :for J=1 to len(A\$)\2
3500     :X\$=mid(A\$,J,1)
3600     :mid(A\$,J,1)=mid(A\$,len(A\$)-J+1,1)
3700     :mid(A\$,len(A\$)-J+1,1)=X\$
3800     :next J
3900    :else
4000     :for J=len(A\$) to I+1 step -1
4100     :if mid(A\$,J,1)>X\$ then cancel for:goto 4300:endif
4200     :next J
4300     :mid(A\$,I,1)=mid(A\$,J,1)
4400     :mid(A\$,J,1)=X\$
4500     :for J=1 to (len(A\$)-I)\2
4600     :X\$=mid(A\$,I+J,1)
4700     :mid(A\$,I+J,1)=mid(A\$,len(A\$)-J+1,1)
4800     :mid(A\$,len(A\$)-J+1,1)=X\$
4900     :next J
5000   return

finds 1, 7 and 8.

The zero was included among the digits even though it would lead to two permutations with a leading zero; even so, none were found with that allowance.

A modification to print the prime factors of the six permutations gives

` 178:     2  89 187:     11  17 718:     2  359 781:     11  71 817:     19  43 871:     13  67`

 Posted by Charlie on 2005-03-21 15:15:26

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