On the difference between consecutive numbers prime to $n$. II.

• DOI: 10.5486/pmd.1965.12.1-4.06
• Publication Date: 2022-11-21T13:54:48Z
• Authors: Christopher Hooley
• Keywords: 510.mathematics; Article

using t h roughou t where poss ible the no t a t i on of II . In I I it was shewn tha t the d i s t r ibu t ion of A i q~(n)/n was app rox ima te ly tha t of a g a m m a var iable wi th p a r a m e t e r 1. This suggests the more general ques t ion of the d i s t r ibu t ion of g roups of t consecut ive intervals Ai . . . . . A~+t-1 and, in par t icu lar , the ques t ion whether the d is t r ibut ions of consecutive intervals be in some sense s ta t is t ical ly independent . If, as might be conjec tured on general grounds , the answer to the la t te r were in the aff irmative, one would have app rox ima te ly