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Large gaps between consecutive prime numbers containing square-free numbers and perfect powers of prime numbers

Authors: Helmut Maier and Michael Th. Rassias
Journal: Proc. Amer. Math. Soc. 144 (2016), 3347-3354
MSC (2010): Primary 11P32
Published electronically: February 17, 2016
MathSciNet review: 3503703
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  • [1] Alina Carmen Cojocaru and M. Ram Murty, An introduction to sieve methods and their applications, London Mathematical Society Student Texts, vol. 66, Cambridge University Press, Cambridge, 2006. MR 2200366 (2006k:11184)
  • [2] K. Ford, D. R. Heath-Brown, and S. Konyagin, Large gaps between consecutive prime numbers containing perfect powers, In: Analytic Number Theory. In honor of Helmut Maier's 60th birthday, (eds. C. Pomerance and M. Th. Rassias), Springer, New York, 2015, pp 83-92.
  • [3] P. X. Gallagher, A large sieve density estimate near $ \sigma =1$, Invent. Math. 11 (1970), 329-339. MR 0279049 (43 #4775)
  • [4] H. Halberstam and H.-E. Richert, Sieve methods, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], London-New York, 1974. London Mathematical Society Monographs, No. 4. MR 0424730 (54 #12689)
  • [5] G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 5th ed., The Clarendon Press, Oxford University Press, New York, 1979. MR 568909 (81i:10002)
  • [6] D. R. Heath-Brown, The least square-free number in an arithmetic progression, J. Reine Angew. Math. 332 (1982), 204-220. MR 656864 (83i:10057),
  • [7] Helmut Maier, Chains of large gaps between consecutive primes, Adv. in Math. 39 (1981), no. 3, 257-269. MR 614163 (82g:10061),
  • [8] R. A. Rankin, The Difference between Consecutive Prime Numbers, J. London Math. Soc. S1-13, no. 4, 242. MR 1574971,

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Additional Information

Helmut Maier
Affiliation: Department of Mathematics, University of Ulm, Helmholtzstrasse 18, 8901 Ulm, Germany

Michael Th. Rassias
Affiliation: Department of Mathematics, ETH-Zürich, Rämistrasse 101, 8092 Zürich, Switzerland – and – Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000

Received by editor(s): May 14, 2015
Received by editor(s) in revised form: September 25, 2015, and October 23, 2015
Published electronically: February 17, 2016
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2016 American Mathematical Society

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