Question 1068756
The even digits cannot be used,
because they would cause at least one of the 2-digit sequences to be even.
Similarly, the digit 5 cannot be used,
because it would cause at least one of the 2-digit sequences to be a multiple of 5.
The digits 3 and 9 cannot be used at the same time,
because they would cause at least one of the 2-digit sequences to be a multiple of 3 (39 or 93).
The two-digit sequences made with 1, 3, and 7 are all (all 6) in the list of prime numbers,
so {{{3!=6}}} 3-digit ABC sequences can be made with 1, 3, and 7.
Using 9, along with 1 and 7, we can also make {{{6}}} 3-digit ABC sequences, .
but {{{3}}} of the resulting ABCA sequences contain the non- prime 2-digit number {{{91=7*13}}} (at the beginning, middle or end).
So there are {{{6+6-3=highlight(9)}}} four-digit  numbers that satisfy the condition in the problem.