The following problem appeared as ENIGMA 1168 in New Scientist 5 January 2002
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 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?