Question

Given 3 distinct digits, six distinct numbers can be formed in such
a way that each of the given digits appears exactly once in any
of them (e.g. using 1; 2; 5 you can form 125; 152; 215; 251; 512; 521).
Is it possible to choose the 3 digits in such a way that all the six
numbers so formed, are prime numbers ?

Answer 1

i don't think so.
you cannot use 2, 4, 5, 6 for sure, because if you do one of the numbers will end in either 2, 4 5 or 6 and hence not be prime.
that leaves 1, 3, 7 , 9
you cannot use 1,3, 7 because 731=17*47
you cannot use 1, 3, 9 because 319 = 11*29

that leaves you with only a 1, 7 , 9 or 3, 7 ,9 to check

Answer 2

Thanks. 791 is 7*113, and 793 is 13*61.
And 731 is 17*43