Re: @Dan 55
"A public key is the product of two large primes" - Flocke Kroes.
It's not usually as simple as that; and if you are thinking of the RSA cryptosystem the public key is an exponent and a modulus, whilst the private key is another exponent (and the same modulus).
I may be missing something here but ... when you ssh to a router, you check the public key is the one that you expect, then you store it. So, the small problem is that, as they all have the same public key, you could mistakenly recognise another router for your own. But the big problem is that they all have the same private key, as you said. So if you go and buy a router at the shop, and extract its private key, you now have the private key for tens of thousands of routers, rather than just for the router you have purchased.