Enigma 1168: Thrice unfactorised
From New Scientist #2324, 5th January 2002 [link]
I have found a four-digit number such that it is impossible to factorise the numbers formed by its first digit or last digit or first two digits or middle two digits or last two digits or first three digits or last three digits or all four digits. In other words all those eight numbers are prime except that either or both of the single-digit numbers may be unity.
Harry and Tom have also each found such a four-digit number. The four-digit numbers that we have found are all different; but Harry’s number uses the same digits as Tom’s number, though in a different order.
Which four digit number have I found?
This completes the archive of puzzles from 2002.