Some applications of Montgomery's sieve

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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
Issue number1
StatePublished - Feb 1973

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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