By the mid-1800s, mathematician Jakob Kulik had embarked on an ambitious project to find all the primes up to 100 million.Ī stencil used by Kulik to sieve the multiples of 37. Another low-tech but effective approach used stencils to locate the multiples.
To automate the tedious sieving steps, a German mathematician named Carl Friedrich Hindenburg used adjustable sliders to stamp out multiples across a whole page of a table at once. By 1800, independent projects had tabulated the primes up to 1 million. Thanks to his efforts, the primes up to 100,000 were widely circulated by the early 1700s. He was motivated to solve ancient arithmetic problems of Diophantos, but also by a personal quest to organize mathematical truths.
That’s the power of the sieve of Eratosthenes.Īn early figure in tabulating primes is John Pell, an English mathematician who dedicated himself to creating tables of useful numbers. With 168 filtering steps, one can isolate the primes up to 1 million. With eight filtering steps, one can isolate the primes up to 400. Sieving multiples of 2, 3, 5 and 7 leaves only the primes between 1 and 100. If you do this with all numbers from 2 to 100, only prime numbers will remain. First, filter out multiples of 2, then 3, then 5, then 7-the first four primes. Euclid proved the infinitude of primes - they go on forever - but history suggests it was Eratosthenes who gave us the sieve to quickly list the primes. By convention, mathematicians don’t count 1 itself as a prime number. This means that prime numbers can’t be evenly divided by any smaller number except 1. “A prime number is that which is measured by the unit alone,” mathematician Euclid wrote in 300 B.C.
But the core idea of the sieve has not changed in over 2,000 years. It allows today’s computers to find billions of primes in less than a second. This sieving process produced tables of millions of primes in the 1800s. To study primes, mathematicians strain whole numbers through one virtual mesh after another until only primes remain. Why they have captivated mathematicians for millennia? As a mathematician devoted to this “Langlands program,” I’m fascinated by the history of prime numbers and how recent advances tease out their secrets. When the King of Norway presents the award to Langlands in May, he will honor the latest in a 2,300-year effort to understand prime numbers, arguably the biggest and oldest data set in mathematics. Langlands’ research demonstrated how concepts from geometry, algebra and analysis could be brought together by a common link to prime numbers. On March 20, American-Canadian mathematician Robert Langlands received the Abel Prize, celebrating lifetime achievement in mathematics.
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