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Diamond, Harold G. Lou, Shituo 2011-05-07T12:15:58Z 2011-05-07T12:15:58Z 10000-01-01 1990 In Chapter I we shall prove a new upper bound in the linear sieve. Our purpose in Chapter II is to explain our method in greater detail than was done in Chapter I. Let x be a large number. We consider $\pi\sb2$(x)--the number of prime twins not exceeding x. Using the new upper bound in the linear sieve from Chapter I, we shall prove that$$\rm\pi\sb2({x}) 0$ and x $\geq$ x$\sb0(\epsilon),$ where$$\rm H = 2{\prod\limits\sb{p>2}}\left(1-{1\over(p-1)\sp2}\right).$$In the Appendix, various computations cited in the text are given in detail. Made available in DSpace on 2011-05-07T12:15:58Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9021722.pdf: 1658645 bytes, checksum: 7176bdd87e5f392556120f02f21d150f (MD5) Previous issue date: 1990 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:38:53Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:16:16-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI9021722 (UMI)AAI9021722 http://hdl.handle.net/2142/19706 eng Copyright 1990 Lou, Shituo Mathematics A new upper bound in the linear sieve and its applications text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.