Thursday, February 19, 2009

1001

1001 = 7 x 11 x 13.

To test a number for divisibility by any of the three divisors 7, 11, and 13 simultaneously, start by marking off the number to be tested in groups of three digits from the units position. Add the first, third, fifth, . . . groups and take away the total of the second, fourth, . . . groups. The number will be divisible by 7, 11, or 13 if the result is divisble by 7, 11, or 13 respectively.

1001 is the 11th pentatope number.

1001 is the fourth palindromic pentagonal number. The sequence of these numbers runs: 1, 5, 22, 1001, 2882, 15,251, . . .


In many cases, including the title
One Thousand and One Arabian Nights, 1001 is meant to indicate a "big number" and need not be taken literally.

Source:
The Penguin Dictionary of Curious and Interesting Numbers, rev. ed., by David Wells.

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