- 5040 (number)
5040 is a
factorial (1 × 2 × 3 × 4 × 5 × 6 × 7 = 5040), and also ahighly composite number , asuperior highly composite number and acolossally abundant number . It is also the number ofpermutation s of 4 items out of a choice of 10 (10 × 9 × 8 × 7 = 5040). For example, there are 5040 possible 4-digit numbers with all digits different (allowing initial zeroes).If is the
divisor function and is theEuler-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 numbersif and only if theRiemann hypothesis is true.In other fields
Plato suggested that 5040 was the perfect number of citizens in a state, for various reasons including:
* it can be divided by all the numbers 1 to 10 and 12 (and its near neighbour 5038 divides by 11)
* it can be divided by 12 twice over.5040 has been quoted as an important number in some types of
numerology . The sum of the radii of theEarth andMoon in miles is 3960 + 1080 = 5040 (in round figures). Twice this figure (the sum of the diameters, or 10,080) is also the number of minutes in a week (7 days × 24 hours × 60 minutes = 10,080).External links
*
Mathworld [http://mathworld.wolfram.com/PlatosNumbers.html article on Plato's numbers]
* http://www.chakracity.com/intro.html - Numerological analysis of 5040
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