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Complementary, my dear Watson (Posted on 2012-06-22) Difficulty: 4 of 5
A Digit Complementary Prime Pair is defined as a pair of prime numbers in which digits in corresponding positions sum to 0 mod 10, e.g. (4721, 6389).
Out of the 136 existing four digit pairs find at least one pair for each of the following requirements (a to f):
a. a reversible prime pair
b. the two primes contain 8 different digits
c. twin primes
d. both primes contain a permutation of 4 consecutive digits
e. first member of the pair contains the 4 prime digits in order
f. each prime contains 3 digits the same

Source: Charles W. Trigg, JRM 22:2, 1990, p 95-97

Bonus: Find a 50 digit DCPP, satisfying a).

No Solution Yet Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)

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Solution computer solution | Comment 1 of 6

Of course the solution to part e is 2357 8753. The other parts are listed below, with the given part identified. The lower number is shown on the left in all cases.

 1009  9001  a
 1069  9041  a
 1097  9013  a
 1181  9929  f
 1409  9601  a
 1487  9623  b
 1559  9551  a
 1619  9491  a
 1949  9161  a
 2111  8999  f
 2417  8693  b
 2741  8369  b
 2963  8147  b
 2999  8111  f
 3067  7043  a
 3083  7027  a
 3109  7901  a
 3407  7603  a
 3467  7643  a
 3533  7577  f
 3803  7207  a
 3917  7193  a
 4127  6983  b
 4253  6857  d
 4721  6389  b
 5051  5059  c
 5503  5507  c

Sorted by the applicable part:
 
 1009  9001  a
 1069  9041  a
 1097  9013  a
 1409  9601  a
 1559  9551  a
 1619  9491  a
 1949  9161  a
 3067  7043  a
 3083  7027  a
 3109  7901  a
 3407  7603  a
 3467  7643  a
 3803  7207  a
 3917  7193  a
 1487  9623  b
 2417  8693  b
 2741  8369  b
 2963  8147  b
 4127  6983  b
 4721  6389  b
 5051  5059  c
 5503  5507  c
 4253  6857  d
 1181  9929  f
 2111  8999  f
 2999  8111  f
 3533  7577  f
 
If any had satisfied more than one part, that would have been shown, but no instances of this were found.

    5   open "dcompprm.txt" for output as #2
   10   P=999
   20   dim Digpres(9)
   30   while P<9999
   40     P=nxtprm(P)
   50     erase Digpres()
   60     dim Digpres(9)
   70     Ps=cutspc(str(P))
   80     Cps="":Revs="":Revcs=""
   90     Dup=0
  100     for I=1 to len(Ps)
  110       Digpres(val(mid(Ps,I,1)))=Digpres(val(mid(Ps,I,1)))+1
  120       Cps=Cps+cutspc(str((10-val(mid(Ps,I,1)))@10))
  130       Revs=mid(Ps,I,1)+Revs
  140       Revcs=cutspc(str((10-val(mid(Ps,I,1)))@10))+Revcs
  150     next
  160     Consec=0:Triple=0
  170     for I=3 to 9
  180       if Digpres(I)>0 and Digpres(I-1)>0 and Digpres(I-2)>0 and Digpres(I-3)>0 then Consec=1
  200     next
  202     for I=0 to 9
  203       if Digpres(I)=3 then Triple=1
  204       if Digpres(I)>1 then Dup=1
  205     next
  210     Chk=Ps+Cps
  220     for I=1 to len(Chk)-1
  230      if instr(mid(Chk,I+1,*),mid(Chk,I,1))>0 then Dup=1
  240     next
  250     Cp=val(Cps)
  260     Rev=val(Revs)
  270     Revc=val(Revcs)
  280     Anstyp=""
  290     if prmdiv(Cp)=Cp then
  300        :if prmdiv(Rev)=Rev and prmdiv(Revc)=Revc then
  310          :Anstyp=Anstyp+"a"
  320        :endif
  330        :if Dup=0 then
  340          :Anstyp=Anstyp+"b"
  350        :endif
  360        :if nxtprm(P)=Cp or nxtprm(Cp)=P then
  370          :Anstyp=Anstyp+"c"
  380        :endif
  390        :if Consec then
  400          :Anstyp=Anstyp+"d"
  410        :endif
  420        :if Triple then
  430          :Anstyp=Anstyp+"f"
  440        :endif
  450        :if Anstyp>"" and P<Cp then print #2,P;Cp,Anstyp:endif
  460     :endif
  470   wend
  480   close #2


  Posted by Charlie on 2012-06-22 14:41:30
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