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.
Generally patterns like this get more regular as the numbers get bigger not less.
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.
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.