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Mathematics of Computation

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Details of the first region of integers $ x$ with $ \pi \sb{3,2}(x)<\pi \sb{3,1}(x)$

Authors: Carter Bays and Richard H. Hudson
Journal: Math. Comp. 32 (1978), 571-576
MSC: Primary 10-04; Secondary 10H20
MathSciNet review: 0476616
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Abstract: Since the time of Chebyshev [4] there has been interest in the magnitude of the smallest integer x with $ {\pi _{3,2}}(x) < {\pi _{3,1}}(x)$, where $ {\pi _{b,c}}(x)$ denotes the number of positive primes $ \leqslant x$ and $ \equiv c\;\pmod b$. The authors have recently reached this threshold with the discovery that $ {\pi _{3,2}}(608981813029) - {\pi _{3,1}}(608981813029) = - 1$. This paper includes a detailed numerical and graphical description of values of $ {\pi _{3,2}}(x) - {\pi _{3,1}}(x)$ in the vicinity of this long sought number.

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Article copyright: © Copyright 1978 American Mathematical Society