Mathematicians are intrigued by the enigmatic patterns of prime numbers, the basic building blocks of math. While scattered on the number line, primes follow a clear, structured distribution that reveals intriguing patterns. Green and Sawhney recently proved a complex statement regarding a specific type of prime, showcasing the power of indirect reasoning and unexpected connections to different mathematical tools. By loosening constraints and exploring rough primes, they were able to advance understanding of prime patterns significantly. Their work not only deepens comprehension of primes but also highlights the potential of the Gowers norm as a versatile tool in number theory.
https://www.quantamagazine.org/mathematicians-uncover-a-new-way-to-count-prime-numbers-20241211/