Here is a gap in a famous series of papers.

G.H. Hardy, and J.E Littlewood
Some problems in Partitio Numerorum,  VII

Their series of papers "Partitio Numerorum" is quite influential in the development of the 
Hardy-Littlewood circle method.

Some comments on the missing part are on page 253 in a paper by 
R.C. Vaughan, Hardy's legacy to number theory,
Journal of the Australian Mathematical Society (Series A) (1998), 
65: 238-266. Cambridge University Press

http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=4937088