by Nick MacKinnon
A 10 digit telephone number (not starting with a ’0?) uses all ten digits once and is written as five two digit numbers.
These five numbers are in increasing order, none share a common factor, one of them is a fourth power and their product is divisible by four of the first five primes.
Another phone number has the same properties except that it is written as two five digit numbers and its second digit is twice that of the second digit of the first number.
What are the two telephone numbers?