Enigma 1566: Consistently older
21 February 2012
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From New Scientist #2729, 10th October 2009 [link]
Yesterday was Harry’s birthday and also Tom’s birthday. Harry is the older. Harry’s current age, Tom’s current age and the difference between their ages are each the product of two primes. The six primes are all different.
Before Harry reaches the age of 90, there will be three further years during which his age, Tom’s age and the difference between their ages will again each be the product of two primes, the six primes all being different.
What is Harry’s current age?