What’s “inside” a black hole? Are they portals to another universe, or are actually other universes in miniature? Those are fringe theories, but no one knows for certain. The incredibly heavy objects’ event horizons — the point past which nothing can escape their powerful gravitational pull, not even information itself — preclude us from knowing their interior secrets.
Physics predicts that a point of infinite density called a singularity resides at their center, which would seem impossible, and yet it’s the best explanation that science currently has to offer.
But mathematics offers another avenue for probing the nature of these cosmic enigmas, and some theorists argue that they can be described in terms of something most of us haven’t given much thought to since grade school: prime numbers. Prime number “particles,” in fact, could swirl at their center, as outlined in a new piece in Scientific American on this emerging research.
“I’d say many high-energy physicists don’t actually know much about that side of number theory,” Eric Perlmutter, a physicist at the Institute of Theoretical Physics in France, told the magazine.
A quick refresher on prime numbers: they’re natural numbers, or positive whole numbers, that can’t be divided into smaller natural numbers. They can only be divided by one and by themselves. Crucially, that means every number can be expressed as a product of primes, making them fundamental units of mathematics; as SciAm explains, that makes prime numbers an analog to the “fundamental particles” in physics, which can’t be broken down further.
Interest in prime numbers stems from the Riemann hypothesis, a conjecture that predicts the seemingly random distribution of prime numbers: if you count primes out in order, 2, 3, 5, 7, 11, 13, and so on, there’s no obvious pattern on when they pop up. Despite being a cornerstone of number theory since German mathematician Bernhard Riemann proposed it in 1859, the hypothesis has never been solved. (The person who does would win a million-dollar prize.)
Over 120 years later, physicist Bernard Julia jumped on the idea to imagine a fundamental, non-interacting particle with energy levels tied to prime numbers. He called these “primons” which in a group became a “primon gas.” And he further discovered that the function used to describe their properties was the same as the Riemann zeta function, a central facet behind the Riemann hypothesis.
Primons remain theoretical, but recent research suggests that they may not just be purely mathematical inventions. A study published in 2025 led by Cambridge physicists revealed that the quantum realm near a black hole singularity organized itself into a “conformal” pattern of prime numbers, like a cloud of primon gas. In a follow up paper, the researchers speculated that if the universe had five dimensions instead of the traditional four, a singularity could only be described with the help of even more exotic “Gaussian” prime numbers.
“We don’t know yet whether the appearance of prime number randomness close to a singularity has a deeper meaning,” Sean Hartnoll, the Cambridge physicist who led the research, told SciAm. “However, to my mind, it is very intriguing that the connection extends to higher dimensional theories of gravity,” including some candidates for a fully quantum mechanical theory of gravity.
Perlmutter, who published his own work using Riemann’s ideas to describe quantum gravity, is optimistic about where the field’s headed.
“The kinds of things we’re trying to understand, black holes in quantum gravity, are surely governed by some beautiful structures,” he told the magazine. “And number theory seems to be a natural language.”
More on space: Physicists Think They Saw a Black Hole Explode
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