I don't know how much sense this post will make (I'm thinking as I post), but here I go:
-All events in our lives - big and small - are ultimately the result of a mind-numbing row of coincidental events. To use a hyperbole; I would not be writing this post if my great-great-great grandfather hadn't agreed to go to that specific trip and met my great-great-great grandmother who almost couldn't make it either, and if my great-great grandmother hadn't chosen to ride a bike to work that particular day she wouldn't have broken her leg and therefore met my great-great grandfather who was her doctor that day, and if my great grandfather hadn't moved to another county when he was 25, he wouldn't have met my great grandmother, and if my grandmother had died of asphyxiation at birth as she was moments away from doing, she wouldn't have lived to meet my grandfather, and if my father hadn't worn a helmet when he ran off the road on his motorbike at age 18 he wouldn't have lived to meet my mother.
All of the events above had to be in place for me to be alive and have the exact personality I have. Add to that a couple of billion other coincidences that make up my family's history and the things that have influenced me in my own life.... What are the odds that I am me?
Well - there are no odds on that, because it's looking at it bass-ackwards; all those things didn't happen in order to create me - I happened to become me as a result of all those coincidental events.
So life is already full of coincidences. Some we notice, most we don't. You got hit by a car today - - - - but if you had remembered to take out the garbage before you left the house, you would have spent a couple of minutes on that, and the car would have missed you because of it.
As for numbers - yes, I agree it seems too far fetched that this could happen as a coincidence. I guess it all comes down to interpretation. I think I have a few of these events in my life as well. Like all the times I would hear a scripture at the hall, and when I was to find it in the Bible, I would immediately open the book on the correct page number and my eyes would look straight at the correct passage. Or like the time I was fed up with it raining, and for fun "shouted": "Stop it!" - and only seconds later the rain was reduced to a trickle, and then stopped.
I see it as coincidences - you may see it as spiritual events.
Something I initially forgot to add here, are lottery numbers. Lotteries are good examples of coincidences happening. Let's say a friend of yours was put in another room from you, and was asked to write down 12 numbers. Then you were given the task of writing down 12 numbers as well. How amazing wouldn't it be if he came back to the room you were in, and it turned out you had written down the exact same numbers that he had!? But that's exactly what happens in a lottery. Granted, there are perhaps several thousand or even millions of people who enter the lottery, and so the odds of someone among them getting it right are lower. But to the person who wins, it's a big coincidence that he/she wrote down the exact same numbers that the lottery people had chosen as the winning numbers.
Another thing I've been thinking about lately (last couple of years) is all the times a coincidence almost happens but doesn't. Like looking at the phone and thinking of my parents. Nothing happens. But what if - by coincidence - they were to call me at that exact moment? Wow, it would blow me away, right? I think there are lots of those 'almost coincidences' throughout our everyday life, but for obvious reasons we only notice them when they actually happen.
Then again - who knows; there are lots of weird things in science today as well, like in quantum mechanics theory. Maybe we'll have an answer that goes beyond coincidences one day (and 'beyond' the spiritual). Most people experience deja-vu. Maybe it's something like that, and that it has an explainable origin other than what I described above. So - even though I view myself as an atheist and naturalist, I wouldn't completely poo-poo what those who feel they have spiritual experiences experience. But as of right now, I must say I think it's just coincidences, even though it sometimes may appear to be too far fetched and the odds seem to be against it.