Prime numbers are the atoms of mathematics, the building blocks of numbers. Yet these indivisible numbers still represent one of the biggest mysteries to the mathematician. As of 2006 the biggest prime we can find has just over 9 million digits. However already two thousand years ago, the Ancient Greeks proved there are infinitely many of these numbers. The challenge for the mathematicians of 2024 is to find a way to show where the primes are hiding. Can the next generation discover a way to efficiently produce large prime numbers?
In recent decades there has been progress towards understanding the mystery of the primes with connections to geometry and quantum physics. We now have more idea where to look for a solution than any other generation since the Ancient Greeks. So it is not implausible that by 2024, the enigma of the primes might finally have been cracked.
This would have huge implications not just for mathematics but for the modern financial world. Internet codes that protect our credit card numbers rely on prime numbers. The reason these codes are currently uncrackable is because we don’t understand the primes… yet. But who knows what the generation of 2024 might reveal about these elusive numbers.
But there is another lesson here for future generations of policy makers. Blue-sky research in abstract mathematics like the prime numbers underpins many of the real world applications on which our modern world depends. The future of science for the next generation depends on nurturing these seeds even if there don’t appear to be obvious short term rewards. After all the discoveries about primes that underpin Internet codes were made in the depths of the seventeenth century.
Marcus du Sautoy is author of The Music of the Primes: Why an Unsolved Problem in Mathematics Matters (buy this book from Amazon (UK) or Amazon (USA)). See his website