Monash physicists find that waves can help us better understand prime numbers

understand prime numbers

Is there a relationship between seemingly random prime numbers and the physical world?
A study published today by Monash physicists in Physical Review Letters, suggests there might be.

The research team, including second author PhD candidate Matthew Ceko, was interested in whether simple wave superposition could give rise to the prime number sequence.

Lead study author Monash physicist Dr Timothy Petersen said a wide variety of prime number sieves had been demonstrated using simple wave superposition.

Physical examples were chosen to easily locate prime numbers in frequency, space, and time, placing constraints on the architecture of the source wave distributions.

The research shows how the cryptic arrangement of prime numbers (2,3,5,7,11,13,17....) can arise from simple superposition (adding together) of waves in basic diffraction.

Using a wave-optical analogue for the ancient sieve of Eratosthenes, the researchers show that many different types of prime sequences can be created in this way, employing elementary diffraction physics.

Proposed experiments could be as simple as adding together identical waves diffracting from double-slit, triple-slit, quadruple-slit... and so on.... apparatus.

“To this day, the seemingly disordered arrangement of primes remains an elusive mathematical puzzle in number theory,” said Dr Timothy Petersen.

“Yet, as building blocks of all integers, the ordering of the prime sequence must obey very strict rules,” he said.

“We hope that these insights will fuel new approaches for tackling this unresolved problem or simply espouse the aesthetic joy of the prime number riddle and elementary diffraction physics.”

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