In order to determine with this sieve all primes between 1 and 100, for example, one has to write down the list of numbers in numerical order and start crossing them out in a certain order: first, the multiples of 2 (except the 2); then, the multiples of 3, except the 3; and so on, starting by the next number that had not been crossed out. The numbers that survive this procedure will be the primes. The method can be formulated as an algorithm.
But now, Helfgott has found a method to drastically reduce the amount of RAM required to run the algorithm:
Helfgott was able to modify the sieve of Eratosthenes to work with less physical memory space. In mathematical terms: instead of needing a space N, now it is enough to have the cube root of N.
So what will be the impact of this? Will we see cheaper, lower-power encryption devices? Or maybe quicker cracking times in brute force attacks?
“This is one of the dirty little secrets of healthcare,” said Gerald Kominski, director of the UCLA Center for Health Policy Research. “If your insurance has a high deductible, you should always ask the cash price.”
Cash prices are intended for uninsured patients — and are frequently still much higher than insured rates. But cash prices for many common procedures have come down thanks to changing regulations and consumers increasingly being able to shop around for cheaper providers. Blood tests can be performed at CVS MinuteClinics and other pharmacies, for instance. Or as I reported a few years ago, MRIs are available from independent providers for as little as $300, whereas many hospitals will charge thousands of dollars.
The article’s main example is the case where the cost for blood tests, through insurance, was more than $80, while the cash price was only $15, and was still sufficient for the lab to make a profit.
Stupidity, like virtue, is its own reward.