As kids, we are taught about the existence of prime numbers: numbers that are only divisible by themselves and one. The first few are easy to recognize just by counting: two, three, five… But the larger the counting goes, the less obvious the prime. The ability to predict where the prime numbers lay on the number line has haunted mathematicians and scientists for centuries, but we may finally have an answer. If we do, it would be disastrous for modern computer security.
The clearest way to understand the distribution of prime numbers is to prove the Riemann hypothesis. This hypothesis was made in 1859 by Bernhard Riemann regarding the behavior of a function called the Riemann zeta function. The behavior of some functions are very well known: a line has a constant slope, sines and cosines repeat their values. But the Riemann zeta function jumps around irregularly. Knowing where this function equals zero tells us something about where the prime numbers are. If the hypothesis is correct, only a quick calculation is necessary to locate prime numbers. Recently, esteemed mathematician Sir Michael Atiyah claims he has a proof. His peers must meticulously check the proof before confirming this discovery. However, his novel approach may spark other ideas of number theory research even if incomplete.
A correct proof would be revolutionary. Prime numbers are essentially the building blocks of mathematics, and understanding their nature could lead to new insights. Many other mathematical predictions hinge on the hypothesis and could finally be proven. Beyond mathematics, encryption could become obsolete. Data is encrypted with the product of large prime numbers known as the public key. If you can factorize the public key and select the right prime factor, you can decrypt and read the message. This process relies on the difficulty of factorizing massive numbers into large primes. Right now, this factorizing process takes hundreds if not thousands of days, and by the time the hackers get close to solving it, the companies have had ample time to switch to a new public key, forcing hackers to start over. However, the computing power and time to factorize drops dramatically with the proof of the Riemann Hypothesis– thus rendering modern encryption useless.
Managing Correspondent: Cari Cesarotti
Original Article: Not Yet Published; Public Lecture-Youtube
More Reading: The Riemann Hypothesis, explained
Image Credit: MPETRISOR/WIKIMEDIA COMMONS (CC BY-SA 4.0)