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Old 2018-05-14, 16:23   #6
CRGreathouse
 
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Aug 2006

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Well... we should not accept the Cramér conjecture since it's not thought to hold. Mathematicians are divided on what should be true: some think that
CSG_\infty=\limsup \frac{p_{n+1}-p_n}{(\log p_n)^2}
is
\frac{2}{e^\gamma} = 1.1229\ldots
while others think that it is infinite and a few think it may even be between the two. In the 21st century I've only seen nonmathematicians argue that its value should be 1 and I haven't seen anyone hold that it should be between 1 and 2/e^gamma or less than 1.
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