It's definitely not 1PH/s. You can solve the equation yourself and figure out how much hash you need to have in order to expect to find a block in a week:
47643398017 * 2^32 / hash rate = 604800
Hash rate = 338338023070975.95
So, you'd need to have about 338TH/s.
Thanks for the calculation. I really suspected this value to be much higher, I guess it's just bad luck when pools that have this value or more do struggle.
While I don't completely get the math, I do have to ask about the word "expect". Does that mean a 50/50 chance in the week? 95% chance, or what? We've obviously seen pools with 2+ PH that have gone 50 hours between blocks (i.e. bad luck). So it would seem that even with 500 TH you could easily go a week without hitting a block.
That's why I ask about your level of "expectation" in a week (i.e. confidence level).
Let me try and help you with that. First, what do the numbers in my equation mean? Well, it's actually a simplified version (that's accurate enough for the purposes of figuring this out). Let me put in words what I wrote above in numbers:
Current Network Difficulty times a difficulty 1 share divided by your hash rate per second equals a week
In other words, since I know the current network difficulty, what a difficulty 1 share is worth (this is the approximation... I'll post the real values if you want) and how long I want to wait to find a block, I can calculate how much hash power I would need to find a block in that time frame.
So why do I keep using the word "expect"? Because it's probability. As you noted, just because the formula says you should find a block in the given timeframe, there's absolutely no guarantee that you will. In fact, there are formulas for that as well. Take a look at CDF (cumulative distribution function). The CDF will tell us that 98% of all blocks will be found at under 400% luck, about 88% of blocks will be found at under 200% luck. 100% luck is around 64% or so.
So, is 64% the confidence level? It's just another way to express the probabilistic data. Just like a pool with 500TH/s could easily go for a week without hitting a block, so too could that pool hit 2 blocks seconds apart.