TY - JOUR
T1 - Some applications of Montgomery's sieve
AU - Vaughan, R. C.
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 1973/2
Y1 - 1973/2
N2 - 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.
AB - 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.
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U2 - 10.1016/0022-314X(73)90059-0
DO - 10.1016/0022-314X(73)90059-0
M3 - Article
AN - SCOPUS:0003109341
VL - 5
SP - 64
EP - 79
JO - Journal of Number Theory
JF - Journal of Number Theory
SN - 0022-314X
IS - 1
ER -