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Oscillation of Mertens’ product formula

Harold G. Diamond, Janos Pintz (2009)

Journal de Théorie des Nombres de Bordeaux

Mertens’ product formula asserts that p x 1 - 1 p log x e - γ as x . Calculation shows that the right side of the formula exceeds the left side for 2 x 10 8 . It was suggested by Rosser and Schoenfeld that, by analogy with Littlewood’s result on π ( x ) - li x , this and a complementary inequality might change their sense for sufficiently large values of x . We show this to be the case.

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