(Nothing in this post except ultra simple math - feel free to skip it if you already know how many blocks take more than 53 minutes to be mined)

I just happened to spot

this block, 53 minutes after it was created. There was no other block in site ... 53 minutes without any blocked being mined.

Wondered a bit about what the odds for this event are. So here are my (very simple) calculations, in case you were curious.

1. I dug up

this old question, which reminded me Bitcoin block times followed the

exponential distribution. It's basically like radioactive decay - each block has a "halflife time" of 10 minutes.

2. Realized that gamma = 10 minutes, and inputted 53 minutes into the cumulative distribution function.

3. Got 1-(e^-53/10) = 0.005

So, about 5 out of every 1,000 blocks take > 53 minutes to confirm. Nothing unusual about spotting a block like this every now and then.

A few interesting numbers:

1. The chance a block is not found within 10 minutes = 36.7%

2. Not found within 20 minutes = 13.5%

3. 30 minutes = 4.9%

4. 40 minutes = 1.8%

5. 50 minutes = 0.67%

6. An hour = 0.24%

(Divide by e = 2.718 to get the next number in line)

So it should happen roughly 10 times every difficulty period, not too unlikely.

I wonder how often this occurs though

Height Age Transactions

212168 52 minutes 677 25,884.30 BTC Deepbit 260.72

212167 1 hour 34 minutes 535 10,720.04 BTC BTC Guild 243.20

212166 1 hour 30 minutes 501 6,880.35 BTC EclipseMC 326.54

EDIT: Fairly often I guess

212149 (Main Chain) 2012-12-14 05:39:51 00000000000002d26537d9eb939ed212171b45f2d70eccbf5b0d0939ee1e80e2 BTC Guild 189 104.49

212148 (Main Chain) 2012-12-14 05:31:39 000000000000039ca22d7de84a951c305535ec8f08449e5b059575308c266456 BTC Guild 365 226.70

212147 (Main Chain) 2012-12-14 05:33:58 00000000000002b54baa99eb63d0fd8b7e07d8d277be713257a7c23098a99b66 69.121.83.181 300 103.45

Silly timestamps.