[StreakyCobra]

In short 40 is already crazy too many digits for most if not all applications. Yet in the original article they say «Granted, most scientific applications don’t need π beyond a few hundred digits, …». Is there scientific applications where they would really need more than 40? Or is it just the author making some guess?

[bostonpete]

The linked NASA article points out that with 40 digits of pi you could compute the circumference of the visible universe to an accuracy equal to the diameter of a hydrogen atom. I'm gonna say there's no practical application that would require even 40 digits, never mind a few hundred

[rlanday]

You need more digits than that to accurately compute double-precision trigonometric functions (if the input is close to pi, you need enough accurate digits left after performing range reduction).

This paper claims you need 2/pi accurate to 1144 bits which is about 345 decimal digits: https://www.csee.umbc.edu/~phatak/645/supl/Ng-ArgReduction.p...

[ectospheno]

As a counterpoint, no real computation I've performed on a computer needed to compute the cos of 2^1023 radians. I can't imagine such a scenario either.

[rlanday]

You can either implement the functions accurately or inaccurately. Implementing them inaccurately is a slippery slope. Intel botched the hardware implementations in their processors not only for large inputs but also for inputs nearish to multiples of pi:

http://notabs.org/fpuaccuracy/index.htm

[fghtr]

>Is there scientific applications where they would really need more than 40? Or is it just the author making some guess?

It is still not clear whether Pi is a normal number or not [0]. Such calculations could in principle give an insight here.

[0] https://en.wikipedia.org/wiki/Pi#Irrationality_and_normality

[WilliamEdward]

Whether there's a use for 40 digits or 40 trillion digits, needing more accuracy is not why we find these numbers. There's no 'need' for this at all. The same way there's no 'need' to find bigger prime numbers. We're just seeing how far we can go, maybe seeing a new pattern emerge.

[klohto]

> The same way there's no 'need' to find bigger prime numbers.

From cryptography standpoint, there is always a need to find bigger prime number. I wouldn't compare this with a Pi.

[benchaney]

Finding bigger prime numbers has no impact on cryptography at all.

The large prime numbers needed for cryptography are a few hundred digits long. The are generated by picking a random numbers and checking it’s neighbors for primality.

The largest prime numbers that have been discovered have millions of digits. Finding a larger prime would have no effect whatsoever on our ability to quickly generate primes with a few hundred digits.

[frutiger]

How does finding a bigger prime help or hinder cryptography? And with many forms of cryptography (e.g. DH kex, ECC) primes only enter as the modulus of the modular arithmetic where being larger is usually not particularly helpful.

[XorNot]

Finding a change in the behavior of Pi that emerges at high precisions would be a significant discovery.

[mhh__]

But it's only 9s after the 762nd digit?

[klohto]

Absolutely! I'm not disputing that it's not "interesting", just that I wouldn't compare Pi number search to prime number search.