This coin should be called Cunningham Chain Coin or Bi Twin Coin instead of Primecoin.
It finds chains of prime numbers and helps advance prime number theory and cryptography. Besides, Primecoin such a snazzy name.
The ridiculous part about Primecoin is that it's built to cripple GPU mining - if somebody launched a similar currency that wasn't restricted it would blow Primecoin away when it comes to advancing prime number theory. Beyond that, dedicated single-purpose machines could leapfrog anything Primecoin has uncovered in a matter of hours. The entire concept is nothing more than a gimmick, in my opinion.
The dev team went out of their way to make Primecoin less efficient.
It was not built to be GPU inefficient. It just turns out their plenty of prime # code available already optimized for CPUs which they used to make the reference miner. Making the GPU miner from scratch is difficult. There is one now actually made by mtrlt but it is inefficient and requires much more optimization.
Why do haters gotta hate?
I'm not hating -- as a currency, I don't have any issues with it. I'm just saying that, in its current form, Primecoin is a pretty inefficient way to discover prime numbers...so while the "prime" aspect of it makes it different...it's really more of a gimmick than anything. I'm not suggesting nobody mine it...but it's not really the dual-purpose knockout punch many would like people to believe.
I welcome anything different...but I think the hype has gone a bit far on Primecoin. In my opinion, it's being billed as something more than it truly is.
I'll try one last rebuttle.
Primecoin miner was never meant to find new prime #s (it theoretically could but highly improbable). It is meant to find cunningham chains and bi-twin chains. Why are these useful?
1. It helps to advance prime number theory
2. Has uses in cryptography
*3. Much like Bitcoin has led to the creation of ASICs for SHA256 and more efficient ways to solve SHA256, if primecoin were to become popular, then effort would be put into making hardware optimized for find prime numbers and chains of prime numbers. Creating more efficient circuit designs for numbers research has scientific merit far beyond just finding chains of prime numbers. Primecoin provides a motivation for such research.
There may very well be more useful PoWs, just noone has come up with one which meets the dual criteria of being difficult to compute but easy to verify which is required for a bitcoin-like coin.