Find five 11-digit pandigital primes P<Q<R<S<T that can be written in a column so that each of the first 10 columns of digits has 5 distinct digits.
Find the set with smallest T.
I tried to make a list of prime candidates in a couple of ways, but it is far too slow.
So what might work is to assume that P,Q,R,S,T begin with 1,2,3,4,5 respectively.
The smallest pandigital prime starting with 5 is 50112346789; set this to T. Now picture the 5x11 grid of digits. The bottom row is 50112346789. The first column is 12345.
Make a loop to try the 10*9*8*7 = 5040 ways the other 4 digits in each column can occur. This is for columns 2 through 10. And in the final column each of rows 1 to 4 could end in 1,3,7,9 in order to be prime.
So 5040*9*4 = 181440 ways the grid could be filled out.
Check to see if any of these have P,Q,R,S being pandigital primes.
If no luck then try the next largest pandigital prime starting with 5.
I suspect this will be faster than a brute force listing of all 11 digit pandigital primes.
|
|
Posted by Larry
on 2023-08-10 22:23:48 |
An idea
