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 Prime Time Revisited (Posted on 2004-10-22)
Do there exist three 2-digit primes such that:
• Any two of the three, averaged, produce another prime, and
• The average of all three is prime

 See The Solution Submitted by SilverKnight Rating: 2.6250 (8 votes)

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 UBASIC program | Comment 8 of 17 |
(In reply to Sieve of Eratosthenes (solution) by Penny)

5   dim Pr(25)
10   P=9
20   while P<100
30      P=nxtprm(P)
40      if P<100 then:I=I+1:Pr(I)=P
50   wend:print
60   NumPr=I
200   for I=1 to NumPr-2
210    for J=I+1 to NumPr-1
212    Av1=(Pr(I)+Pr(J))/2
215    if nxtprm(Av1-1)=Av1 then
220    :for K=J+1 to NumPr
222     :Av2=(Pr(I)+Pr(K))/2:Av3=(Pr(J)+Pr(K))/2
225     :if nxtprm(Av2-1)=Av2 and nxtprm(Av3-1)=Av3 then
230     :Av=(Pr(I)+Pr(J)+Pr(K))/3
240     :if Av=int(Av) then
250       :if nxtprm(Av-1)=Av then print Pr(I),Pr(J),Pr(K),Av:endif
255      :endif
257     :endif
260    :next
270    next
280   next

finds

11      47      71      43.0 (the latter being the average)

 Posted by Charlie on 2004-10-22 15:40:33

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