What’s “inside” a black hole? Are they portals to another universe, or are they actually microcosms of other universes? These are fringe theories, but no one knows for sure. The event horizons of these extremely heavy objects – the point beyond which nothing, not even information itself, can escape their powerful gravitational pull – prevent us from understanding their inner secrets.
Physics predicts the existence of an infinite density point at their center called a singularity, which seems impossible, but it’s the best explanation science has to offer at the moment.
But mathematics offers another way to explore the nature of these cosmic mysteries, and some theorists believe they can be described by something most of us haven’t considered since grade school: prime numbers. In fact, prime number “particles” can spin around their centers, as a new article outlines scientific american About this emerging research.
“I would say that many high-energy physicists actually don’t know much about this aspect of number theory,” Eric Perlmutter, a physicist at France’s Institute for Theoretical Physics, told the magazine.
A quick refresher on prime numbers: they are natural numbers, or positive integers, that cannot be divided into smaller natural numbers. They are only divisible by one and themselves. Crucially, this means that every number can be expressed as a product of prime numbers, making them the fundamental unit of mathematics; as Academy of Sciences Explain that this makes prime numbers similar to “elementary particles” in physics that cannot 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 the prime numbers in order, 2, 3, 5, 7, 11, 13, and so on, there is no obvious pattern to when they appear. Although this hypothesis has been a cornerstone of number theory since it was proposed by German mathematician Bernhard Riemann in 1859, it has never been solved. (Whoever does this will win a million-dollar prize.)
More than 120 years later, physicist Bernard Julia immediately proposed the idea, imagining a fundamental, non-interacting particle with energy levels related to prime numbers. He called these “primons,” and together they became “primon gas.” He further discovered that the function used to describe their properties was the same as the Riemann zeta function, a core part behind the Riemann hypothesis.
Primons are still theoretical, but recent research suggests they may be more than purely mathematical inventions. A study led by Cambridge physicists published in 2025 showed that the quantum field near a black hole’s singularity organizes itself into “conformal” patterns of prime numbers, like a cloud of proton gas. In a follow-up paper, the researchers speculated that if the universe had five dimensions instead of the traditional four, then singularities could only be described with the help of more exotic “Gaussian” primes.
“We don’t yet know whether the emergence of randomness in prime numbers close to singularities has deeper significance,” said Cambridge physicist Sean Hartnoll, who led the study. Academy of Sciences. “However, it seems to me very interesting that this 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 the development of the field.
“The things we are trying to understand, black holes in quantum gravity, are certainly governed by some beautiful structure,” he told the magazine. “Number theory seems to be a natural language.”
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