On the lcm of the differences of eight primes
Author:
François Morain
Journal:
Math. Comp. 52 (1989), 225229
MSC:
Primary 11A41; Secondary 11A07, 11Y05
Corrigendum:
Math. Comp. 54 (1990), 911.
Corrigendum:
Math. Comp. 54 (1990), 911.
MathSciNet review:
971409
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Following C. A. Spiro, who has found eight primes for which we show that for every set of eight odd primes , one has . Moreover, infinitely often, under the assumption of the 8tuple conjecture.
 [1]
Egon
Balas and Chang
Sung Yu, Finding a maximum clique in an arbitrary graph, SIAM
J. Comput. 15 (1986), no. 4, 1054–1068. MR 861370
(88f:05058), http://dx.doi.org/10.1137/0215075
 [2]
G.
H. Hardy and J.
E. Littlewood, Some problems of ‘Partitio numerorum’;
III: On the expression of a number as a sum of primes, Acta Math.
44 (1923), no. 1, 1–70. MR
1555183, http://dx.doi.org/10.1007/BF02403921
 [3]
D.
R. HeathBrown, The divisor function at consecutive integers,
Mathematika 31 (1984), no. 1, 141–149. MR 762186
(86c:11071), http://dx.doi.org/10.1112/S0025579300010743
 [4]
Donald
E. Knuth, The art of computer programming, 2nd ed.,
AddisonWesley Publishing Co., Reading, Mass.LondonAmsterdam, 1975.
Volume 1: Fundamental algorithms; AddisonWesley Series in Computer Science
and Information Processing. MR 0378456
(51 #14624)
 [5]
Ian
Richards, On the incompatibility of two
conjectures concerning primes; a discussion of the use of computers in
attacking a theoretical problem, Bull. Amer.
Math. Soc. 80
(1974), 419–438. MR 0337832
(49 #2601), http://dx.doi.org/10.1090/S000299041974134348
 [6]
C. A. Spiro, The Frequency with Which an IntegralValued, PrimeIndependent, Multiplicative or Additive Function of n Divides a Polynomial Function of n, Ph. D. Thesis, University of Illinois, UrbanaChampaign, 1981.
 [1]
 E. Balas & C. S. Yu, "Finding a maximum clique in an arbitrary graph," SIAM J. Comput., v. 15, 1986, pp. 10541068. MR 861370 (88f:05058)
 [2]
 G. H. Hardy & J. E. Littlewood, "Some problems of 'Partitio Numerorum'; III: On the expression of a number as a sum of primes," Acta Math., v. 44, 1923, pp. 170. MR 1555183
 [3]
 D. R. HeathBrown, "The divisor function at consecutive integers," Mathematika, v. 31, 1984, pp. 141149. MR 762186 (86c:11071)
 [4]
 D. E. Knuth, "Sorting and Searching", in The Art of Computer Programming, vol. III, AddisonWesley, Reading, Mass., 1973. MR 0378456 (51:14624)
 [5]
 I. Richards, "On the incompatibility of two conjectures concerning primes; A discussion of the use of computers in attacking a theoretical problem," Bull. Amer. Math. Soc., v. 80, 1974, pp. 419438. MR 0337832 (49:2601)
 [6]
 C. A. Spiro, The Frequency with Which an IntegralValued, PrimeIndependent, Multiplicative or Additive Function of n Divides a Polynomial Function of n, Ph. D. Thesis, University of Illinois, UrbanaChampaign, 1981.
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
11A41,
11A07,
11Y05
Retrieve articles in all journals
with MSC:
11A41,
11A07,
11Y05
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198909714096
PII:
S 00255718(1989)09714096
Article copyright:
© Copyright 1989 American Mathematical Society
