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Millennial Conference on Number Theory
May 21-26, 2000
University of Illinois
Urbana, IL, USA

Organizers
B.C. Berndt, N. Boston, H.G. Diamond, A.J. Hildebrand, W. Philipp

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Upper bounds for the number of long prime tuples
by
Christian Elsholtz
TU Clausthal (Germany)

We use a combined large sieve method to prove upper bounds for the number of conceivable prime k-tuples, for large k. For example we prove that there are at most O(x5/6) such k-tuples of size k=(log x)2. The heuristic Bateman-Horn formula is apparently not applicapble for such tuples.

Date received: January 11, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadx-10.