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Researcher Modifies Sieve of Eratosthenes To Work With Less Physical Memory Space (scientificamerican.com)
grcumb writes: Peruvian mathematician Harald Helfgott made his mark on the history of mathematics by solving Goldbach's weak conjecture, which states that every odd number greater than 7 can be expressed as the sum of three prime numbers. Now, according to Scientific American, he's found a better solution to the sieve of Eratosthenes: "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: "Now, inspired by combined approaches to the analytical 100-year-old technique called the circle method, 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? Mathematician Jean Carlos Cortissoz Iriarte of Cornell University and Los Andes University offers an analogy: "Let's pretend that you are a computer and that to store data in your memory you use sheets of paper. If to calculate the primes between 1 and 1,000,000, you need 200 reams of paper (10,000 sheets), and with the algorithm proposed by Helfgott you will only need one fifth of a ream (about 100 sheets)," he says.
*sigh*
Getting tired of "news" posting _zero_ details.
Does anyone have details on the actual algorithm? Reference Implementation?
Getting tired of "news" posting _zero_ details.
I'd be happier if the meagre details they do post were at least correct. If one fifth of a ream is 100 sheets then 200 reams is 100,000 sheets not 10,000 as the summary states.
"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?"
Neither.
It's a method to discover primes using elimination of non-primes up to the square root of the number you're after.
If you can get that far, you can get to the prime itself quite easily. It's not going to help discover new large primes without eliminating BILLIONS of numbers in between.
And from there it has nothing to do with cracking encryption whatsoever.
The impact of this is that a child's method of eliminating factorisable numbers slowly takes up slightly less storage space (i.e. slightly less variables held in RAM) than before. It's not a breakthrough in maths, but a slight efficiency saving in the computer science to perform the algorithm in practical terms.