3 ms·

Unless it's not. I'm sure lots of mathematicians have open bets about that. I still remember my supervisor hoping for no Higgs "because then physics will be bo

by quchen 3y ago

Unless it's not. I'm sure lots of mathematicians have open bets about that. I still remember my supervisor hoping for no Higgs "because then physics will be boring for the foreseeable future".

Spivak 3y ago
I think anyone that's betting on it being false is nuts at this point. It would be astounding if it held for the first three trillion then broke down. Generally patterns like this get more regular as the numbers get bigger not less.
- kongolongo 3y ago
  Here's a hypothesis: no positive number is evenly divisible by 3 trillion one. True up to 3 trillion then false at 3 trillion 1.
- Extigy 3y ago
  It can happen, the Pólya conjecture is the usual example which holds until n = 906150257. Another fun one I just found is the statement “n^17 + 9 and (n + 1)^17 + 9 are relatively prime”. The first counterexample is at n=8424432925592889329288197322308900672459420460792433.
  - dilippkumar 3y ago
    How does one even find something like this? Let alone prove that this is the first counterexample. That number looks to be in the order of the age of the universe in millionths of a quectosecond!!
- deleted 3y ago
  [deleted]
- NeoTar 3y ago
  https://en.m.wikipedia.org/wiki/Skewes%27s_number https://en.m.wikipedia.org/wiki/Skewes%27s_number In number theory, Skewes's number is any of several large numbers used by the South African mathematician Stanley Skewes as upper bounds for the smallest natural number x for which the prime-counting function is greater than the logarithmic integral function. The current best estimate we have for when this happens is: 1.397162×10^316 To put that in context... it's such a big number it's hard to put in context - I've been trying to make a physical analogy, but I think its bigger than the number of Planck-length cubes that could fit in the visible universe.
  - amenhotep 3y ago
    Way bigger. The universe is a mere 10^185 Planck volumes.

by quchen 3y ago

Unless it's not. I'm sure lots of mathematicians have open bets about that. I still remember my supervisor hoping for no Higgs "because then physics will be boring for the foreseeable future".

Spivak 3y ago

I think anyone that's betting on it being false is nuts at this point. It would be astounding if it held for the first three trillion then broke down. Generally patterns like this get more regular as the numbers get bigger not less.

kongolongo 3y ago
Here's a hypothesis: no positive number is evenly divisible by 3 trillion one. True up to 3 trillion then false at 3 trillion 1.
Extigy 3y ago
It can happen, the Pólya conjecture is the usual example which holds until n = 906150257. Another fun one I just found is the statement “n^17 + 9 and (n + 1)^17 + 9 are relatively prime”. The first counterexample is at n=8424432925592889329288197322308900672459420460792433.
- dilippkumar 3y ago
  How does one even find something like this? Let alone prove that this is the first counterexample. That number looks to be in the order of the age of the universe in millionths of a quectosecond!!
deleted 3y ago
[deleted]
NeoTar 3y ago
https://en.m.wikipedia.org/wiki/Skewes%27s_number https://en.m.wikipedia.org/wiki/Skewes%27s_number In number theory, Skewes's number is any of several large numbers used by the South African mathematician Stanley Skewes as upper bounds for the smallest natural number x for which the prime-counting function is greater than the logarithmic integral function. The current best estimate we have for when this happens is: 1.397162×10^316 To put that in context... it's such a big number it's hard to put in context - I've been trying to make a physical analogy, but I think its bigger than the number of Planck-length cubes that could fit in the visible universe.
- amenhotep 3y ago
  Way bigger. The universe is a mere 10^185 Planck volumes.