4 ms·
> It ain't as pretty as just between straight integer multiples, but the fact that it exists in some shape at all is cool! Actually: the form that Larsen prove
by vitus 4y ago
> It ain't as pretty as just between straight integer multiples, but the fact that it exists in some shape at all is cool!
Actually: the form that Larsen proved is stronger than "for sufficiently large X, there is at least one Carmichael number between X and 2X".
So with the more specific proof, he also proved the simpler statement that's easier to express.
- renewiltord 4y agoHaha very good!
- gnubison 4y agoWhat is the stronger version?
- renewiltord 4y agoBertrand's postulate is that there is at least one prime between x and 2x for x>=1 Daniel Larsen's result here is that there are e^((log x)/((log log x)^(2+d))) Carmichael numbers between x and (x + x/((log x)^(1/(2+d)))) for x>=X (depends on d) e^((log x)/((log log x)^(2+d))) is >= 1 for all x >= 1. (x + x/((log x)^(1/(2+d)))) <= 2x Stronger by being tighter than the (x,2x) bound and being more specific about the >= 1 number of Carmichael numbers
- gnubison 4y agoThank you!