I remember reading that the devs were considering implementing the Primecoin hashing algo as one of the auxPoW hashing algo's in a myriad of chains. Why not implement the
Riecoin algo instead or as well of as one of the three chains minimum that are needed to run a myriad properly.
How is Riecoin different from Primecoin?
Primecoin uses the Fermat primality test, which has some flaws. Carmichael numbers are not prime and still pass Fermat's test for all bases, however those are relatively rare. Secondly, in general, if Fermat's test says a number is prime, it has at least a 50% probability of being prime. Primecoin uses only one Fermat test with base 2. While base 2 may provide more confidence than the general bound of 50%, still many composites will pass as primes. What's worst, is that Euler-Lagrange-Lifchitz test used for the other primes in the chain assumes the previous number in the chain is prime. So if the chain starts with a number that is not prime, then the Euler-Lagrange-Lifchitz test is not guaranteed to work, and all numbers in the chain may be composite.
Short version: Primecoin numbers are not guarranteed to be prime, they may be Fermat pseudoprimes to the base 2. There is an infinite list of Fermat pseudoprimes to the base 2 (oeis.org/A001567). Riecoin uses enough Rabin-Miller tests with random bases, so the probability of a number that is not prime being accepted by the majority of the Riecoin network is negligible.
We propose the n/s "range explored (numbers) per second" metric instead of pps (primes per second) or shorter-chains per second. This is the quantity of numbers tested (whether by sieve of explicit primality test) and discarded as not constituting a valid PoW per second. While it is still difficult to compare this number for different difficulties, it is a much better metric: it can be used to meaningfully compare different algorithms, hardware speed, etc as long as you have the same diff. More n/s always means more blocks. For example a mining rig would be advertised as having X n/s@minimum diff. Something similar like "multipliers per second" might be possible for Primecoin, but it wouldn't scale as well when difficulty grows. In Primecoin, PPS is "just for fun" and shorter chains per second may not be accurate to compare the performance of algorithms for full-length chains per second.
Assuming the Riemann Hypothesis and the Hardy-Littlewood k-tuple conjectures are true, by using Hardy-Littlewood constants a miner can estimate the average time before a block is found, allowing profit calculations and to estimate the computing power of the network.
In Primecoin there is no practical way of estimating the time before finding a block, moreover difficulty 10.1 is easier than 9.9 making it impossible to estimate how secure the network is.
A centralized checkpoint system is implemented inside Primecoin. While it is disabled by default, if FUD about attacks start to spread, I believe some people will panic and enable it. A centralized checkpoint allows its controllers to perform double spends without any need for any % of hash rate. Can we be sure it will not be hacked and/or abused?
Riecoin is capped to a fixed amount of coins (84M), but Primecoin has no limit. While it is arguable, we believe our deflationary model - similar to Bitcoin's - is better.
1min block speed would bloat the blockchain and create more orphans, stales. We have 2.5min which was tested for years in LTC. I don't know of any 1min coin that has years of testing. I think it's not true that 1min is fast enough for waiting in a line when you buy a coffee: with blocks targeted each minute, you have a 1 in 150 chance of having to wait more than 5 minutes for a block, this would still be unacceptable for some coffee stores. Also, with 2.5 each block requires more work, meaning we will have larger prime numbers sooner.
