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:

    In a number of other cultures, fathers are not relegated to babysitter status, nor is their ability to be primary nurturers so readily dismissed.... We have evidence that in our own society men can rear and nurture their children competently and that men’s methods, although different from those of women, are imaginative and constructive.
    Kyle D. Pruett (20th century)

    We have our little theory on all human and divine things. Poetry, the workings of genius itself, which, in all times, with one or another meaning, has been called Inspiration, and held to be mysterious and inscrutable, is no longer without its scientific exposition. The building of the lofty rhyme is like any other masonry or bricklaying: we have theories of its rise, height, decline and fall—which latter, it would seem, is now near, among all people.
    Thomas Carlyle (1795–1881)