5040 (number) - Number Theory

Number Theory

If is the divisor function and is the Euler-Mascheroni constant, then 5040 is the largest known number for which this inequality holds:

.

This is somewhat unusual, since in the limit we have:

Guy Robin showed in 1984 that the inequality fails for all larger numbers if and only if the Riemann hypothesis is true.

Read more about this topic:  5040 (number)

Famous quotes containing the words number and/or theory:

    Strange goings on! Jones did it slowly, deliberately, in the bathroom, with a knife, at midnight. What he did was butter a piece of toast. We are too familiar with the language of action to notice at first an anomaly: the ‘it’ of ‘Jones did it slowly, deliberately,...’ seems to refer to some entity, presumably an action, that is then characterized in a number of ways.
    Donald Davidson (b. 1917)

    Everything to which we concede existence is a posit from the standpoint of a description of the theory-building process, and simultaneously real from the standpoint of the theory that is being built. Nor let us look down on the standpoint of the theory as make-believe; for we can never do better than occupy the standpoint of some theory or other, the best we can muster at the time.
    Willard Van Orman Quine (b. 1908)