Prime numbers — whole numbers divisible only by themselves and one — are often described as the “fundamental particles” of mathematics, the indivisible building blocks from which every other whole number is made. A small but intriguing line of recent theoretical physics suggests these same numbers may also surface in one of nature’s most extreme settings: the chaotic physics near the centre of a black hole. The connections are speculative and early-stage, but they hint that the mathematics governing primes might echo in the laws of gravity.
The number-theory backdrop
The deepest open question about primes is the Riemann hypothesis, set out by Bernhard Riemann in 1859. Riemann gave a formula whose first term closely estimates how many primes lie below a given number, while a second term — built from the Riemann zeta function and the locations where it equals zero — corrects that estimate. Why those “zeta zeros” consistently refine the count is the heart of the hypothesis, which remains unproven and carries a $1 million Clay Mathematics Institute prize for whoever settles it.
From “primons” to black holes
The idea that physics might encode primes is not new. In the late 1980s the physicist Bernard Julia imagined a hypothetical particle whose energy levels are the logarithms of the prime numbers — a “primon” — and showed that the partition function of a gas of such particles is exactly the Riemann zeta function. For decades that remained an elegant curiosity. More recently, physicists including Sean Hartnoll at the University of Cambridge, working with collaborators, brought the concept into a concrete gravitational model. Studying the turbulent dynamics that arise as spacetime collapses toward a singularity, they found a repeating, self-similar scaling structure — reminiscent of the way patterns recur at different sizes in the art of M. C. Escher — and showed it could be described by a quantum system whose spectrum is organised around prime numbers, an analogue of Julia’s primon gas.
A later preprint added a twist: extending the analysis from the usual four dimensions to five forced the appearance of “Gaussian primes,” a generalisation of primes that includes an imaginary component (a number multiplied by the square root of −1). Separately, the physicist Eric Perlmutter, of the Institute of Theoretical Physics at Saclay, has proposed reframing the zeta zeros so that the techniques of number theory can be applied more broadly to problems in quantum gravity.
How seriously to take it
These results are best understood as an emerging research direction rather than settled science. They are drawn largely from preprints and idealised models, the gravitational scenarios are simplified, and the appearance of prime-based structure does not amount to a proof of any link to the Riemann hypothesis itself. As one of the researchers quoted in the reporting notes, many high-energy physicists are not deeply versed in this corner of number theory, so the dialogue between the two fields is only beginning. What makes the work compelling is not a finished theory but a recurring hint — that the “alphabet” mathematicians use to study primes may also be a natural language for describing extreme gravity. The original feature appears in Scientific American, with additional coverage from Live Science.
