On the distribution of pseudoprimes
Author:
Carl Pomerance
Journal:
Math. Comp. 37 (1981), 587593
MSC:
Primary 10A21; Secondary 10A20
MathSciNet review:
628717
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Abstract 
References 
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Additional Information
Abstract: Let denote the pseudoprime counting function. With we prove for large x, an improvement on the 1956 work of Erdös. We conjecture that .
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Carl
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 [1]
 N. G. de Bruijn, "On the number of positive integers and free of prime factors . II," Nederl. Akad. Wetensch. Proc. Ser. A, v. 69, 1966, pp. 239247.
 [2]
 E. R. Canfield, P. Erdös & C. Pomerance, "On a problem of Oppenheim concerning "Factorisatio Numerorum"," J. Number Theory. (To appear.) MR 1876176 (2002j:11012)
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 P. Erdös, "On pseudoprimes and Carmichael numbers," Publ. Math. Debrecen, v. 4, 1956, pp. 201206. MR 0079031 (18:18e)
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 P. Erdös, "On the sum ," Israel J. Math., v. 9, 1971, pp. 4348. MR 0269613 (42:4508)
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 C. Pomerance, "Popular values of Euler's function," Mathematika, v. 27, 1980, pp. 8489. MR 581999 (81k:10076)
 [6]
 C. Pomerance, "A new lower bound for the pseudoprime counting function," Illinois J. Math. (To appear.) MR 638549 (83h:10012)
 [7]
 C. Pomerance, J. L. Selfridge & S. S. Wagstaff, Jr., "The pseudoprimes to ," Math. Comp., v. 35, 1980, pp. 10031026. MR 572872 (82g:10030)
 [8]
 R. A. Rankin, "The difference between consecutive prime numbers," J. London Math. Soc., v. 13, 1938, pp. 242247.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198106287170
PII:
S 00255718(1981)06287170
Keywords:
Pseudoprime,
Carmichael number,
Euler's function
Article copyright:
© Copyright 1981
American Mathematical Society
