Imagine this discovery led to a larger breakthrough on prime numbers that allowed easy factorization of large integers and effectively rendered public key cryptography such as RSA ineffective overnight, by allowing anyone with a consumer-grade CPU to crack any production-size key.

Does the industry have DR plans for this scenario? Can the big players quickly switch to a different, unbroken encryption system? While it would probably be a heavenly day for jailbreakers, console modders and other "device freedom" types generally, the overall impact would be disastrous and incalculable.

Does the industry simply not consider "sudden number theory breakthrough" a possible event?

People always think the structure of primes is complex, but it's not really, it's just a recursive structure of the magnitude gaps not landed on by multiples of previous gaps.

It doesn't make it easier to "predict" without tracking all prior gaps, but it's not essentially a complex structure. Kind of funny that like such a simple structure is so elusive. Sorta like how the 3n + 1 sequence gives rise to such complexity. Or the logistic map with its parameter above the threshold.

Something inspiring about this: "In dedicated Friday afternoon thinking sessions, he returned to the problem again and again over the past decade, to no avail."

> “At first sight, they look pretty random,” says James Maynard, a mathematician at the University of Oxford. “But actually, there’s believed to be this hidden structure within the prime numbers.”

What would the pattern of primes hypothetically look like? Is there expected to be some kind of closed form formula? If the Riemann hypothesis were proven, what would be the next step to understanding the distribution? Or is the proof itself expected to hold this answer?

## throwaway81523 ·1 days ago

https://www.quantamagazine.org/sensational-proof-delivers-ne...

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## EMIRELADERO ·1 days ago

Imagine this discovery led to a larger breakthrough on prime numbers that allowed easy factorization of large integers and effectively rendered public key cryptography such as RSA ineffective overnight, by allowing anyone with a consumer-grade CPU to crack any production-size key.

Does the industry have DR plans for this scenario? Can the big players quickly switch to a different, unbroken encryption system? While it would probably be a heavenly day for jailbreakers, console modders and other "device freedom" types generally, the overall impact would be disastrous and incalculable.

Does the industry simply not consider "sudden number theory breakthrough" a possible event?

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## keepamovin ·1 days ago

It doesn't make it easier to "predict" without tracking all prior gaps, but it's not essentially a complex structure. Kind of funny that like such a simple structure is so elusive. Sorta like how the 3n + 1 sequence gives rise to such complexity. Or the logistic map with its parameter above the threshold.

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## timmb ·1 days ago

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## huyvanbin ·1 days ago

What would the pattern of primes hypothetically look like? Is there expected to be some kind of closed form formula? If the Riemann hypothesis were proven, what would be the next step to understanding the distribution? Or is the proof itself expected to hold this answer?