I would say that it's almost a sham - not in the sense that it's worthless, just that it markets to people who are apt to exaggerate its worth. Let's consider a few of the things that people might do with such 'bought' primes: they might try to decrypt something, encipher something, or have some sort of sentimental value for a particular prime.
First: trying to decrypt something by buying lists of 400 digit primes. It seems to me that somehow, we have figured out that a message is enciphered using a 400 digit prime (likely the product of that prime and another, larger prime). We are trying to brute force attack it - but how many 400 digit primes are there? By the prime number theorem, we know there are about $\frac{x}{\log x} $ primes up to x, so we consider $\dfrac{10^{400}}{400 \log 10} - \dfrac{10^{399}}{399 \log 10}$, which is of the order $10^{398}$. Even if the list had each of these primes on it, just trying them all out is computationally improbable (to be... generous). It's akin to saying: we know this door is locked by a key of about this size, so let's get every such key in the world and try them.
Secondly: we are trying to encipher something. I will assume that we are going to use some public key cryptography and are trying to come up with something incoveniently large to decrypt, perhaps using RSA. But then we will probably use 2 primes, resulting in a number of over 800 digits. That's annoyingly large. Worse, it is very easy to find your own 400 digit prime. One would expect to find one at random, by checking consecutive odd 400 digit numbers, every thousandth guess or so ($1/{400 \log 10}$ numbers on average need to be checked, not counting the consideration of only even numbers). One would assume that needing such incredible security would mean that you at least own a computer, and therefore have the capabilities of finding your own large primes.
Thirdly, sentimental value. This reminds me of the 'Name a Star after Someone' campaign, like here. The author John Allen Paulos, I think, once quipped in his book Innumeracy that he should like to offer to name numbers after people, maybe charging more for prime numbers, etc.
But in regards to your fear of buying a number that someone else has bought - suppose that they choose 100 different 400 digit primes randomly for each list they sell. Then it wouldn't be until something like their $10^{200}$th sale that we would expect someone to have bought the same number as you. However, if we consider this instead like the same-birthday 'paradox,' this number would be several dozen orders of magnitude reduced, and yet still meaninglessly large. There's isn't enough money in the world to get to that level.
In fact, they could name a different 400 digit prime after each human, every day, for longer than our sun will be around. I should start selling primes on ebay.
But the awards for computing larger and larger primes are not because of the use of the resulting prime number, but instead because it inspires development of computational and algorithmic methods. Finding large primes quickly becomes very, very challenging. I believe the current awards is for a prime of 100,000,000 digits, a very challenging number even to store in a computer's memory, let alone manipulate.
Here is a hypothesized real-world application, but it's not by humans...it's by cicadas.
Cicadas are insects which hibernate underground and emerge every 13 or 17 years to mate and die (while the newborn cicadas head underground to repeat the process). Some people have speculated that the 13/17-year hibernation is the result of evolutionary pressures. If cicadas hibernated for X years and had a predator which underwent similar multi-year hibernations, say for Y years, then the cicadas would get eaten if Y divided X. So by "choosing" prime numbers, they made their predators much less likely to wake up at the right time.
(It doesn't matter much anyway, because as I understand it, all of the local bug-eating animals absolutely gorge themselves whenever the cicadas come out!)
EDIT: I should have refreshed my memory before posting. I just re-read the article, and the cicadas do not hibernate underground. They apparently "suckle on tree roots". The article has a few other mild corrections to my answer, as well.
Best Answer
I may be a bit jaded, but I don't think there are a whole lot of applications that will impress someone 10 years old. I tell college students (in a class for future educators, no less!) that their ability to shop safely online depends on prime numbers, and hardly get a reaction.
So, I'd take a different approach: Mystery and intrigue.
It's hard for anyone who hasn't studied math seriously to understand what mathematics is about, but most people believe we have it pretty well figured out (and if not, the Bigger and Better Computer of Tomorrow (TM) will surely have it all straightened out in a few years, right?). Which is why it should be surprising that we really don't understand prime numbers very well!
That's a bit of a stretch, of course. We know a lot about prime numbers, but the biggest (or at least most famous) open question in all of mathematics, the Riemann Hypothesis (I wouldn't even mention the name, let alone give any details!) is a belief about prime numbers. Another big-hitter (again, fame-wise; I can't fathom why it would be important to anyone) is the Goldbach Conjecture, another belief concerning prime numbers. This one could easily be stated to 5th graders, and they could verify that it's true for any numbers they pick out.
If the million dollar bounty for the Riemann Hypothesis is still in effect and you knew everything there was to know about prime numbers, you'd walk away with a cool million dollars! That's how much more we want to know about prime numbers, because we just don't know certain things!
The point is this. It's easy to define a prime number, and easy to work with prime numbers. But when we start asking certain questions, we just don't know. Nobody does. A handful of incredible mathematicians know a bit more than most, but even the most well-informed people on earth only know incrementally more than your students, when it comes to prime numbers. (Again: obviously a stretch. This really applies to isolated statements about prime numbers, but we're trying to sell here, not be pedantic).
I'll also mention that when we talked about the Sieve of Eratosthenes for finding prime numbers (again in the class for future educators), I remarked that this method is over two-thousand years old (older than many popular Western religions). Fast forward to now, and our best methods for listing all prime numbers in a certain range are only incrementally better. Cooler still, these better methods all use this basic sieving technique at their core! So we're better at listing primes because we're better at sieving, but not that much better -- in two thousand years!
Your 5th graders could easily sieve, and use the primes they find to verify Goldbach's Conjecture for tons of numbers. They'd be playing the game of mathematics then, getting their hands dirty in a completely self-sufficient way. And it can be phrased as a challenge: "I bet you can't write 138 as a sum of two primes!"
So the big moral of the story is that, to mathematicians, primes are mysterious, shiny objects. I wouldn't focus on their shininess, only the mystery. They have such mysterious facets that, in some ways, we're not much better at understanding them than we were thousands of years ago.