Sunday Times Teaser 2527
by Graham Smithers
Published: 27 February 2011 (link)
Without repeating a digit I wrote down two five-figure numbers. For the first of these, its first two digits form a number divisible by two, its first three digits form a number divisible by three, and likewise for four and five. For the second number, looking again at the numbers formed by the first few digits, those of prime length are prime and the one of length four is a square. Furthermore the sum of the digits of the difference between the two numbers is itself a digit. Without doing much division you should now be able to answer the question:
What are the two five-figure numbers?