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Turns out, Primes are in P
zorba1 writes "Manindra Agrawal et. al. of the Indian Institute of Technology Kanpur CS department have released a most interesting paper today. It presents an algorithm that determines whether a number is prime or not in polynomial time. While I haven't gone through the presentation in detail, it looks like a promising, albeit non-optimized, solution for the famous PRIMES in P problem."
Thank you. I'm glad someone finally pointed out that we already have a classical (as opposed to quantum) probabilistic algorithm for determining primality. Every other fool on this board is running around wearing his/her tin hat and shouting about RSA being defunct. All this does is push primality testing from the BPP complexity class into the P complexity class. It is significant in the sense that it weakens the argument for BPP being larger than P.
Of course, we also have a polynomial-time algorithm for prime factorization (Shor's Algorithm). It's just that it requires a quantum computer, which is difficult to build. So far, the biggest number factored is 15... 1024 bit keys will be safe for a while yet. I believe it's 15 - 20 years until they're broken, if Moore's Law holds for quantum computers in terms of maximum number of qubits possible (so far, it roughly has, but then, we're only at about 7 qubits).
It's the Sieve of Eratosthenes. A number n is of size log(n). This is a deterministic algorithm; why bring up NP? What is the time complexity of division? And here's a hint: you start with n-digit (n=100) numbers and present an algorithm that runs in time 10^n. This is in P?
Has anyone actually read the paper? The algorithm is outlined, with a complexity analysis. Don't forget, P-time doesn't mean usable.
Unlimited growth == Cancer.