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 Near Goldbach Alphametics (Posted on 2009-06-10)
In the following alphametic equation each capital letter in bold represents a different base x digit from 0 to x-1. None of the numbers can contain any leading zero.

PRIME + PRIME + PRIME = NUMBER

Determine the minimum positive integer value of x such that PRIME is a prime number.

Bonus Question:

What would have been the minimum positive integer value of x, if each capital letter in bold represented a different base x prime digit from 2 to x-1?

 No Solution Yet Submitted by K Sengupta No Rating

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 program for part 2 Comment 2 of 2 |

Similar to what I used for part 1, but with added requirement:

10   dim Psn(20)
100         dim Used(100)
190   kill "goldbach.txt"
200         open "goldbach.txt" for output as #2
300         cls
400         for X=8 to 45
500           Psn(1)=1
600   for J=2 to 6
700    Psn(J)=Psn(J-1)*X
800   next
900   :for P=2 to X-1:if prmdiv(P)=P then
1000   :Used(P)=1
1100   :for N=2 to X-1:if prmdiv(N)=N then
1200   :if Used(N)=0 then
1300   :Used(N)=1
1400   :for R=2 to X-1:if prmdiv(R)=R then
1500   :if Used(R)=0 then
1600   :Used(R)=1
1700   :for I=2 to X-1:if prmdiv(I)=I then
1800   :if Used(I)=0 then
1900   :Used(I)=1
2000   :for M=2 to X-1:if prmdiv(M)=M then
2100   :if Used(M)=0 then
2200   :Used(M)=1
2300   :for E=2 to X-1:if prmdiv(E)=E then
2400   :if Used(E)=0 then
2500   :Used(E)=1
2600   :Prime=P*Psn(5)+R*Psn(4)+I*Psn(3)+M*Psn(2)+E
2700   :for U=2 to X-1:if prmdiv(U)=U then
2800   :if Used(U)=0 then
2900   :Used(U)=1
3000   :for B=2 to X-1:if prmdiv(B)=B then
3100   :if Used(B)=0 then
3200   :Used(B)=1
3300   :Number=N*Psn(6)+U*Psn(5)+M*Psn(4)+B*Psn(3)+E*Psn(2)+R
3400   :if 3*Prime=Number and prmdiv(Prime)=Prime then
3500   :print X,P;R;I;M;E,N;U;M;B;E;R,Prime;Number
3600   :print #2,X,P;R;I;M;E,N;U;M;B;E;R,Prime;Number
3700   :endif
3800   :Used(B)=0:endif
3900   :endif
4000   :next
4100   :Used(U)=0:endif
4200   :endif
4300   :next
4400   :Used(E)=0:endif
4500   :endif
4600   :next
4700   :Used(M)=0:endif
4800   :endif
4900   :next
5000   :Used(I)=0:endif
5100   :endif
5200   :next
5300   :Used(R)=0:endif
5400   :endif
5500   :next
5600   :Used(N)=0:endif
5700   :endif
5800   :next
5900   :Used(P)=0:endif
6000   :next
6100   :next
6200   :close
6300

checked up to base 45 and didn't find any answers.

 Posted by Charlie on 2009-06-11 16:03:12

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