New maximal prime gaps and first occurrences

Author:
Thomas R. Nicely

Journal:
Math. Comp. **68** (1999), 1311-1315

MSC (1991):
Primary 11A41; Secondary 11-04, 11Y11, 11Y99

DOI:
https://doi.org/10.1090/S0025-5718-99-01065-0

Published electronically:
February 13, 1999

MathSciNet review:
1627813

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Abstract | References | Similar Articles | Additional Information

Abstract: The search for first occurrences of prime gaps and maximal prime gaps is extended to . New maximal prime gaps of 806 and 906 are found, and sixty-two previously unpublished first occurrences are found for gaps varying from 676 to 906.

**1.**D. Baugh and F. O'Hara, Letters to the Editor,*Large Prime Gaps*and*and More*, J. Recreational Math**24:3**(1992) 186-187.**2.**R. P. Brent,*The first occurrence of large gaps between successive primes*, Math. Comp.**27:124**(1973), 959-963. MR**48:8360****3.**R. P. Brent,*The first occurrence of certain large prime gaps*, Math. Comp.**35:152**(1980), 1435-1436. MR**81g:10002****4.**C. Caldwell,*The Prime Page*, at http://www.utm.edu/research/primes/.**5.**H. Cramér,*On the order of magnitude of the difference between consecutive prime numbers*, Acta Arith.**2**(1937), 23-46.**6.**M. Deleglise and J. Rivat,*Computing : The Meissel, Lehmer, Lagarias, Miller, Odlyzko Method*, Math. Comp.**65**(1996), 235-245. MR**96d:11139****7.**H. Dubner, private e-mail communication, 4 August 1996.**8.**H. Dubner, private e-mail communication, 2 September 1996.**9.**H. Dubner and H. Nelson,*Seven consecutive primes in arithmetic progression*, Math. Comp.**66**(1997), 1743-1749. MR**98a:11122****10.**L. J. Lander and T. R. Parkin,*On the first appearance of prime differences*, Math. Comp.**21**(1967), 483-488. MR**37:6237****11.**T. R. Nicely,*Enumeration to of the twin primes and Brun's constant*, Virginia Journal of Science**46:3**(1995), 195-204. MR**97e:11014****12.**T. R. Nicely, unpublished document, available at http://www.lynchburg.edu/public/academic/math/nicely/pentbug/pentbug.txt.**13.**P. Ribenboim,*The little book of big primes*, Springer-Verlag, New York, 1991. MR**92i:11008****14.**H. Riesel,*Prime numbers and computer methods for factorization*, 2nd ed., Birkhäuser, Boston, 1994. MR**95h:11142****15.**D. Shanks,*On maximal gaps between successive primes*, Math. Comp.**18**(1964), 646-651. MR**29:4745****16.**S. Weintraub,*A prime gap of 864*, J. Recreational Math.**25:1**(1993), 42-43.**17.**J. Young and A. Potler,*First occurrence prime gaps*, Math. Comp.**52:185**(1989), 221-224. MR**89f:11019****18.**J. Young, private e-mail communication, 6 June 1996.

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Additional Information

**Thomas R. Nicely**

Affiliation:
Department of Mathematics, Lynchburg College, 1501 Lakeside Drive, Lynchburg, Virginia 24501-3199

Email:
nicely@acavax.lynchburg.edu

DOI:
https://doi.org/10.1090/S0025-5718-99-01065-0

Keywords:
Prime numbers,
prime gaps,
first occurrences,
maximal gaps,
maximal prime gaps

Received by editor(s):
June 16, 1997

Received by editor(s) in revised form:
December 5, 1997

Published electronically:
February 13, 1999

Article copyright:
© Copyright 1999
American Mathematical Society