What's the Number?

Jan 22, 2012

Ray: This is short and sweet. I’m going to give you a series of numbers and ask you what the next number in the series is. Here are the numbers: 4, 6, 12, 18, 30, 42, 60 and then X.
Here is a hint. You may notice all the numbers I’ve given you are even numbers. Here’s another hint. The number after the number I’m looking for is 102.

What is the number?
RAY: Here's the answer. Now usually when you have a puzzle like this, there’s an operation involved, you add two, multiply by three, subtract four, your grandmother’s age divided by 6 and you get the next number.  But, this isn’t one of those puzzles, there’s no operator involved.  And the hint I gave, of course, was that they’re all even numbers, which means they’re flanked or surrounded by odd numbers.  So, for example, number 42 has an odd number on either side of it.  Right? 
TOM:  Yeah.
RAY:  Number 60 has an odd number on either side of it. 
TOM:  Got it.
RAY: The blank number is probably going to have an odd number on either side of it. And these numbers aren’t just odd, they’re kind of extra odd because they are prime numbers. So, the number 42 is flanked by 41 and 43, which are both prime. The number 60 is flanked by 59 and 61, both of which are prime.
The number we are looking for, the blank, is flanked by two prime numbers and it happens to be 72.  And it’s flanked by 71 and 73, as is 102, which I gave as the bonus number, which is flanked by 101 and 103.  Pretty cute, eh? 
Do we have a winner?
TOM:  Yes, we do!  Our winner this week is Joe Belmont from Franklin, Wisconsin.
RAY:  You lucky devil, Joe!

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