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March 10, 2005
The Human Element - 100 Interesting Number Facts
My friend Ted (inventor of System Administrator's Day) sent me this list of interesting facts about the natural numbers from 0 to 100. The original list was compiled by Erich Friedman, who has extended it well into the 200s. I suspect it has been floating around the email network for some time, but I think it's really cool. If enough people like this sort of thing, maybe I can get Ferdy to let me post a message about proving Peano's postulates using Von Neumann's pure set numbering representation scheme and a quantifiable theory of types, which I've always found to be a fascinating idea.
- 0 is the additive identity.
- 1 is the multiplicative identity.
- 2 is the only even prime.
- 3 is the number of spatial dimensions we live in.
- 4 is the smallest number of colors sufficient to color all planar maps.
- 5 is the number of Platonic solids.
- 6 is the smallest perfect number.
- 7 is the smallest number of integer-sided rectangles that tile a rectangle so that no 2 rectangles share a common length.
- 8 is the largest cube in the Fibonacci sequence.
- 9 is the maximum number of cubes that are needed to sum to any positive integer.
- 10 is the base of our number system.
- 11 is the largest known multiplicative persistence.
- 12 is the smallest abundant number.
- 13 is the number of Archimedian solids.
- 14 is the smallest number n with the property that there are no numbers relatively prime to n smaller numbers.
- 15 is the smallest composite number n with the property that there is only one group of order n.
- 16 is the only number of the form xy=yx with x and y different integers.
- 17 is the number of wallpaper groups.
- 18 is the only number that is twice the sum of its digits.
- 19 is the maximum number of 4th powers needed to sum to any number.
- 20 is the number of rooted trees with 6 vertices.
- 21 is the smallest number of distinct squares needed to tile a square.
- 22 is the number of partitions of 8.
- 23 is the smallest number of integer-sided boxes that tile a box so that no two boxes share a common length.
- 24 is the largest number divisible by all numbers less than its square root.
- 25 is the smallest square that can be written as a sum of 2 squares.
- 26 is the only number to be directly between a square and a cube.
- 27 is the largest number that is the sum of the digits of its cube.
- 28 is the 2nd perfect number.
- 29 is the 7th Lucas number.
- 30 is the largest number with the property that all smaller numbers relatively prime to it are prime.
- 31 is a Mersenne prime.
- 32 is the smallest 5th power (besides 1).
- 33 is the largest number that is not a sum of distinct triangular numbers.
- 34 is the smallest number with the property that it and its neighbors have the same number of divisors.
- 35 is the number of hexominoes.
- 36 is the smallest number (besides 1) which is both square and triangular.
- 37 is the maximum number of 5th powers needed to sum to any number.
- 38 is the last Roman numeral when written lexicographically.
- 39 is the smallest number which has 3 different partitions into 3 parts with the same product.
- 40 is the only number whose letters are in alphabetical order.
- 41 is the smallest number that is not of the form |2x - 3y|.
- 42 is the 5th Catalan number.
- 43 is the number of sided 7-iamonds.
- 44 is the number of derangements of 5 items.
- 45 is a Kaprekar number.
- 46 is the number of different arrangements (up to rotation and reflection) of 9 non-attacking queens on a 9x9 chessboard.
- 47 is the largest number of cubes that cannot tile a cube.
- 48 is the smallest number with 10 divisors.
- 49 is the smallest number with the property that it and its neighbors are squareful.
- 50 is the smallest number that can be written as the sum of of 2 squares in 2 ways.
- 51 is the 6th Motzkin number.
- 52 is the 5th Bell number.
- 53 is the only two digit number that is reversed in hexadecimal.
- 54 is the smallest number that can be written as the sum of 3 squares in 3 ways.
- 55 is the largest triangular number in the Fibonacci sequence.
- 56 is the number of reduced 5 x 5 Latin squares.
- 57 = 111 in base 7.
- 58 is the number of commutative semigroups of order 4.
- 59 is the smallest number whose 4th power is of the form a4+b4-c4.
- 60 is the smallest number divisible by 1 through 6.
- 61 is the 6th Euler number.
- 62 is the smallest number that can be written as the sum of of 3 distinct squares in 2 ways.
- 63 is the number of partially ordered sets of 5 elements.
- 64 is the smallest number with 7 divisors.
- 65 is the smallest number that becomes square if its reverse is either added to or subtracted from it.
- 66 is the number of 8-iamonds.
- 67 is the smallest number which is palindromic in bases 5 and 6.
- 68 is the lowest uninteresting number, which makes it very interesting.
- 69 has the property that n2 and n3 together contain each digit once.
- 70 is the smallest abundant number that is not the sum of some subset of its divisors.
- 71 divides the sum of the primes less than it.
- 72 is the maximum number of spheres that can touch another sphere in a lattice packing in 6 dimensions.
- 73 is the smallest number (besides 1) which is one less than twice its reverse.
- 74 is the number of different non-Hamiltonian polyhedra with minimum number of vertices.
- 75 is the number of orderings of 4 objects with ties allowed.
- 76 is an automorphic number.
- 77 is the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1.
- 78 is the smallest number that can be written as the sum of of 4 distinct squares in 3 ways.
- 79 is a permutable prime.
- 80 is the smallest number n where n and n+1 are both products of 4 or more primes.
- 81 is the square of the sum of its digits.
- 82 is the number of 6-hexes.
- 83 is the number of zero-less pandigital squares.
- 84 is the largest order of a permutation of 14 elements.
- 85 is the largest n for which 12+22+32+...+n2 = 1+2+3+...+m has a solution.
- 86 = 222 in base 6.
- 87 is the sum of the squares of the first 4 primes.
- 88 is the only number known whose square has no isolated digits.
- 89 = 81 + 92
- 90 is the number of degrees in a right angle.
- 91 is the smallest pseudoprime in base 3.
- 92 is the number of different arrangements of 8 non-attacking queens on an 8x8 chessboard.
- 93 = 333 in base 5.
- 94 is a Smith number.
- 95 is the number of planar partitions of 10.
- 96 is the smallest number that can be written as the difference of 2 squares in 4 ways.
- 97 is the smallest number with the property that its first 3 multiples contain the digit 9.
- 98 is the smallest number with the property that its first 5 multiples contain the digit 9.
- 99 is a Kaprekar number.
- 100 is the smallest square which is also the sum of 4 consecutive cubes.
# At Thu 12:50 PM | Permalink | Trackback URI | Comments (5) | More The Human Element
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I have been given the task of getting links for our websites that have good page rank on the links directories.
In addition we have many categories so your site will be place on an appropriate page.
If you would like to trade links please send me your website details.
P.S.: I got your e-mail publicly listed on your webpage .
Our apologies if you do not wish to take part in a link exchange.
Best Regards,
Marry Tailor
Posted by: Marry Tailor at November 8, 2005 10:43 AM
Posted by: Bryce Herdt at August 20, 2006 3:49 PM
Posted by: Bruce Parrello at August 20, 2006 5:56 PM
Posted by: Naomi at February 19, 2007 8:23 PM
Theoretically, everything on this site that is backed by a link is a factual statement, though it does depend on the accuracy of the source. For example, I used the news story about the revenge burnings in Iraq to underpin my statements about the nature of the ethnic violence there, and that story has since been called into question.
It is a major philosophical problem: outside of mathematics, there's no guarantee that truth is anything more than a shared opinion.
However, there are at least 99 incontrovertible facts on this page, and that qualifies as "many" in anyone's book.
Posted by: Ferdy 
at February 20, 2007 12:40 AM
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