# Sunday Times Teaser 2604 – Foreign Friends

*by Nick MacKinnon*

#### Published: 19 August 2012 (link)

The telephone number of my Japanese friend is a ten-figure number written as a group of five two-figure numbers. The number does not start with a 0, no digit is used more than once, the numbers in the group are in increasing order, no two of them have a common factor, and one of them is a fourth power. Also, the product of the numbers in the group is divisible by four of the first five primes.

The telephone number of my Russian friend is a ten-figure number but it is written as a group of two five-figure numbers. The number and group have the same properties as those stated above. Its second digit is double the second digit of the Japanese number.

What are the two telephone numbers?

Here is my first attempt at a solution (dismally slow):