Some applications of Montgomery's sieve

Research output: Contribution to journalArticle

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Abstract

Artin has conjectured that every positive integer not a perfect square is a primitive root for some odd prime. A new estimate is obtained for the number of integers in the interval [M + 1, M + N] which are not primitive roots for any odd prime, improving on a theorem of Gallagher. Erdo{combining double acute accent}s has conjectured that 7, 15, 21, 45, 75, and 105 are the only values of the positive integer n for which n - 2k is prime for every k with 1 ≤ k ≤ log2n. An estimate is proved for the number of such n ≤ N.

Original languageEnglish (US)
Pages (from-to)64-79
Number of pages16
JournalJournal of Number Theory
Volume5
Issue number1
DOIs
StatePublished - Feb 1973

Fingerprint

Sieve
Primitive Roots
Integer
Odd
Square number
Acute
Estimate
Interval
Theorem

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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Some applications of Montgomery's sieve. / Vaughan, R. C.

In: Journal of Number Theory, Vol. 5, No. 1, 02.1973, p. 64-79.

Research output: Contribution to journalArticle

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