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 Prime with distinct digits (Posted on 2013-09-18)
What is the biggest prime number, no digits repeated if

a. zero can be included?
b. zero is excluded?

 See The Solution Submitted by Ady TZIDON No Rating

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 computer solution | Comment 1 of 2

A 10-digit number with all the different decimal digits will be divisible by 3 as the sum of the digits would be 45, which is divisible by 3. A non-zero digit must be eliminated, so a prime with 9 digits will need to have a zero.

5   P=98700000
10   while P<99000000
30   P=fnNxprime(P)
40   Ps=cutspc(str(P))
50   Good=1
60   for I=1 to len(Ps)-1
70     if instr(mid(Ps,I+1,*),mid(Ps,I,1))>0 then Good=0:cancel for:goto 100
80   next
90   if Good then print P
100   wend
999   end

The last few 9-digit cases are:

987651403
987652301
987653201
987654103

so 987654103 is the highest when zero is included.

The last few 8-digit cases are:

98764321
98765143
98765201
98765413
98765431

which includes the highest without a zero: 98765431.

 Posted by Charlie on 2013-09-18 17:33:46

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