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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
Posted:
February 13, 1999
MathSciNet review:
1627813
Full-text PDF Free Access
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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 New maximal prime gaps of 806 and 906 are found, and sixty-two previously unpublished first occurrences are found for gaps varying from 676 to 906.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.
Richard
P. Brent, The first occurrence of large gaps
between successive primes, Math. Comp. 27 (1973), 959–963.
MR
0330021 (48 #8360), http://dx.doi.org/10.1090/S0025-5718-1973-0330021-0
- 3.
Richard
P. Brent, The first occurrence of certain large
prime gaps, Math. Comp. 35
(1980), no. 152, 1435–1436.
MR 583521
(81g:10002), http://dx.doi.org/10.1090/S0025-5718-1980-0583521-6
- 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.
Deléglise and J.
Rivat, Computing 𝜋(𝑥): the
Meissel, Lehmer, Lagarias, Miller, Odlyzko method, Math. Comp. 65 (1996), no. 213, 235–245. MR 1322888
(96d:11139), http://dx.doi.org/10.1090/S0025-5718-96-00674-6
- 7.
H. Dubner, private e-mail communication, 4 August 1996.
- 8.
H. Dubner, private e-mail communication, 2 September 1996.
- 9.
Harvey
Dubner and Harry
Nelson, Seven consecutive primes in arithmetic
progression, Math. Comp.
66 (1997), no. 220, 1743–1749. MR 1423071
(98a:11122), http://dx.doi.org/10.1090/S0025-5718-97-00875-2
- 10.
L.
J. Lander and T.
R. Parkin, On first appearance of prime
differences, Math. Comp. 21 (1967), 483–488. MR 0230677
(37 #6237), http://dx.doi.org/10.1090/S0025-5718-1967-0230677-4
- 11.
Thomas
R. Nicely, Enumeration to 10¹⁴ of the twin primes and
Brun’s constant, Virginia J. Sci. 46 (1995),
no. 3, 195–204. MR 1401560
(97e:11014)
- 12.
T. R. Nicely, unpublished document, available at http://www.lynchburg.edu/public/academic/math/nicely/pentbug/pentbug.txt.
- 13.
Paulo
Ribenboim, The little book of big primes, Springer-Verlag, New
York, 1991. MR
1118843 (92i:11008)
- 14.
Hans
Riesel, Prime numbers and computer methods for factorization,
2nd ed., Progress in Mathematics, vol. 126, Birkhäuser Boston
Inc., Boston, MA, 1994. MR 1292250
(95h:11142)
- 15.
Daniel
Shanks, On maximal gaps between successive
primes, Math. Comp. 18 (1964), 646–651. MR 0167472
(29 #4745), http://dx.doi.org/10.1090/S0025-5718-1964-0167472-8
- 16.
S. Weintraub, A prime gap of 864, J. Recreational Math. 25:1 (1993), 42-43.
- 17.
Jeff
Young and Aaron
Potler, First occurrence prime gaps,
Math. Comp. 52 (1989), no. 185, 221–224. MR 947470
(89f:11019), http://dx.doi.org/10.1090/S0025-5718-1989-0947470-1
- 18.
J. Young, private e-mail communication, 6 June 1996.
- 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:
http://dx.doi.org/10.1090/S0025-5718-99-01065-0
PII:
S 0025-5718(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
Posted:
February 13, 1999
Article copyright:
© Copyright 1999 American Mathematical Society
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