New maximal prime gaps and first occurrences
Author:
Thomas R. Nicely
Journal:
Math. Comp. 68 (1999), 13111315
MSC (1991):
Primary 11A41; Secondary 1104, 11Y11, 11Y99
Published electronically:
February 13, 1999
MathSciNet review:
1627813
Fulltext PDF Free Access
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 New maximal prime gaps of 806 and 906 are found, and sixtytwo previously unpublished first occurrences are found for gaps varying from 676 to 906.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) 186187.
 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/S00255718197303300210
 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/S00255718198005835216
 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), 2346.
 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/S0025571896006746
 7.
H. Dubner, private email communication, 4 August 1996.
 8.
H. Dubner, private email 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/S0025571897008752
 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/S00255718196702306774
 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T. R. Nicely, unpublished document, available at http://www.lynchburg.edu/public/academic/math/nicely/pentbug/pentbug.txt.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, SpringerVerlag, 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/S00255718196401674728
 16.
S. Weintraub, A prime gap of 864, J. Recreational Math. 25:1 (1993), 4243.
 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/S00255718198909474701
 18.
J. Young, private email 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) 186187.
 2.
 R. P. Brent, The first occurrence of large gaps between successive primes, Math. Comp. 27:124 (1973), 959963. MR 48:8360
 3.
 R. P. Brent, The first occurrence of certain large prime gaps, Math. Comp. 35:152 (1980), 14351436. 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), 2346.
 6.
 M. Deleglise and J. Rivat, Computing : The Meissel, Lehmer, Lagarias, Miller, Odlyzko Method, Math. Comp. 65 (1996), 235245. MR 96d:11139
 7.
 H. Dubner, private email communication, 4 August 1996.
 8.
 H. Dubner, private email communication, 2 September 1996.
 9.
 H. Dubner and H. Nelson, Seven consecutive primes in arithmetic progression, Math. Comp. 66 (1997), 17431749. MR 98a:11122
 10.
 L. J. Lander and T. R. Parkin, On the first appearance of prime differences, Math. Comp. 21 (1967), 483488. MR 37:6237
 11.
 T. R. Nicely, Enumeration to of the twin primes and Brun's constant, Virginia Journal of Science 46:3 (1995), 195204. 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, SpringerVerlag, 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), 646651. MR 29:4745
 16.
 S. Weintraub, A prime gap of 864, J. Recreational Math. 25:1 (1993), 4243.
 17.
 J. Young and A. Potler, First occurrence prime gaps, Math. Comp. 52:185 (1989), 221224. MR 89f:11019
 18.
 J. Young, private email communication, 6 June 1996.
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Additional Information
Thomas R. Nicely
Affiliation:
Department of Mathematics, Lynchburg College, 1501 Lakeside Drive, Lynchburg, Virginia 245013199
Email:
nicely@acavax.lynchburg.edu
DOI:
http://dx.doi.org/10.1090/S0025571899010650
PII:
S 00255718(99)010650
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
