Ancient Greek civilization might have fallen a few thousand years ago, but their philosophy, art and analytical tools remain useful today. In fact, one of the world's top mathematicians believes that an algorithm that makes use of an ancient Greek device called the "sieve of Eratosthenes" could be the key to discovering all-new, inconceivably large prime numbers, reports Science Alert.
Prime numbers have always been a big deal to mathematicians, and ever since Euclid (another ancient Greek) proved the infinitude of the primes, the race has been on to discover the largest ones. There is even a hefty financial incentive for modern number hunters: a $150,000 prize for the person who finds the first 100-million-digit prime.
But it turns out that one oft-overlooked Greek, Eratosthenes, might have held the key to revealing these mega-primes all along. His so-called "sieve" is an ingenious filtering algorithm for finding primes. It works as follows: First, make a list of all the numbers in a certain range, say 1-30. Next, begin with the first prime, which is 2, and cross out every multiple of 2 on the list. After that, work your way up through all the primes. Since 3 is the next prime, cross out all the multiples of 3. After that, do the same for 5 (the next prime after 3). Eventually you'll exhaust your list, having crossed out all the numbers that aren't prime and leaving only the ones that are.
There's never been any reason that this method couldn't reveal any prime of any size, but there's been one problem: for larger numbers, it requires a huge amount of computing memory. Quite simply, it's not efficient. And when you're talking about prime numbers that are tens of millions of digits long, efficiency matters.
Enter Harald Helfgott, a Peruvian mathematician who rose to fame in the math world when he solved a 271-year-old problem called Goldbach's weak conjecture back in 2013. With his sights now set on primes, he has devised a new way to reduce the computing memory required to run the sieve of Eratosthenes by a significant factor.
Mathematician Jean Carlos Cortissoz from Cornell University, who wasn't part of the research, puts Helfgott's method into perspective at Scientific American: "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)."
In fact, the speed of this calculation could be accelerated by using cache memory, which is smaller but faster than RAM.
It's an ambitious proposal. And lucky for Helfgott, Eratosthenes isn't around to share in the prime number prize money. It's a testament to the ingenuity of the ancient Greeks, though, that their methods can still have so much power today.