Zoo of Numbers: Numbers 201 to 684

What's Special About This Number?

Fun facts on numbers (and their strange properties), both mathematical and cultural, tantalising problems and anecdotes. The number facts in this website are also available as features for print and electronic publishing.

is a centered icosagonal number, and a Kaprekar constant in base 4.
201n + 2 are prime, for n = 14, 15, and 16. - Patterson
201 x 627 = 126027
(the product has the same digits as its factors)

= 3 x 67

is the sixth Bell number.

is a square pyramidal number.
is the number of different squares you can find in a chessboard.

= 101 + 103 (sum of twin primes)
= 1² + 2² + 3² + 4² + 5² + 6² + 7² + 8² (sum of consecutive squares)
= 23 + 29 + 31 + 37 + 41 + 43 (sum of consecutive primes)
= 2² x 3 x 17

204² = 23³ + 24³ + 25³

is the largest number that cannot be written as the sum of distinct primes of the form 6n+1.

= 2³ + 2³ + 4³ + 5³ (sum of cubes)

is the smallest number whose English name contains all five vowels exactly once (twO hUndrEd And sIx).

= 1³ + 2³ + 2³ + 4³ + 5³ (sum of consecutive cubes)

is the smallest possible sum of primes which are formed using each of the digits 1 through 9:
207 = 89 + 61 + 43 + 7 + 5 + 2 - Gupta
curiously, the first half of the digits of 207⁴ are a permutation of the last half of the digits: 1836036801.

= 3² · 23
= 2² + 3² + 5² + 13²

CIVIC is a palindrome and the anagram of the Roman numeral CCVII (207).

is a tetranacci number.

= 2⁴ x 13
= 2² + 3² + 5² + 7² + 11² - Sladcik
= 2³ + 2³ + 4³ + 4³ + 4³

is a Harshad number and the smallest quasi-Carmichael number in base 9.
the curve 4²x² - y² = 209 contains the 'prime points' (3, 13), (5, 29), (7, 43), and (13, 83) - Buddenhagen

88 + 209 = 297 and 88,209 = 297² (see number 494 furtherbelow)

= 1⁶ + 2⁵ + 3⁴ + 4³ + 5² + 6¹ - posted by Jim O'Donohoe
= 3³ + 3³ + 3³ + 4³ + 4³
= 11 · 19

is a Chen prime.

= 3⁵ - 2⁵
= 67 + 71 + 73 (sum of consecutive primes)

is the lowest even 3-digit integer, ABC, such that (ABC)/(A x B x B) is also prime.
curiously, 4 out of 5 digits of 212² are the same (44944).
212° Fahrenheit = 100° Celsius (the boiling point of water)

= 6³ + (- 1)³ = 6³ - 1³ (sum and difference of cubes) - G. Sarcone
= 555 in base 6

is the smallest cube which can be written as the sum of 3 cubes: 3³ + 4³ + 5³
= 216 = 6¹⁺²
= 216 = [(2 + 1)!]⁶ (autothecal number)

Is the 'constant' of the smallest multiplication magic square:

is a Gaglütz number: 217 modulo 712 = 217 - G. Sarcone
is a centered hexagonal number, and a Kaprekar constant in base 2.

= 1 + 2 + 4 + 5 + 10 + 20 + 25 + 50 + 100 (sum of the factors of the number 100)
= 1³ + 6³ = (- 8)³ + 9³ (sum of cubes)

is a nontotient number, and the number of 4-vertex digraphs.

= 7³ + 13³ (sum of cubes)

is a semiprime number, and the number of space groups, not including mirror images.

= 3³ + 4³ + 4³ + 4³

is the smallest amicable number.

is the number of 7-vertex Hamiltonian planar graphs.

221b, Baker Street, London, England is the address of Sherlock Holmes.

= 10² + 11²
= 13 x 17
is the sum of 5 consecutive primes: 37 + 41 + 43 + 47 + 53
is also the sum of 9 consecutive primes:
11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41

is a long prime.

the numbers of the series 23, 223, 2223, 22223, 222223, 2222223, 22222223, 222222223, 2222222223... (in the preceding list only 23, 223, and 22222223 are primes) are formed with the formula: (2 x 10ⁿ + 7)/9

= 71 + 73 + 79 (sum of consecutive primes)
= 19 + 23 + 29 + 31 + 37 + 41 + 43

is an octagonal square number.

= 113² - 112²
= (1 + 2 + 3 + 4 + 5)²
= 1³ + 2³ + 3³ + 4³ + 5³
= 3² x 5² = 15 x 15

is a centered pentagonal number.

= 2 x 113
= 2(7² + 8²)

is a prime number and twin prime with 229, it is also the number of 8-edge connected planar graphs.

= 2 + 3 + 5 + 7 + (2 x 3 x 5 x 7) [sum of the sum and the product of the first 4 primes]
= 2³ + 3³ + 4³ + 4³ + 4³
227ⁿ = 233ⁿ + 239ⁿ - 251ⁿ - 257ⁿ + 263ⁿ , with n = 1, 2

2²²⁷ - 1 is the smallest composite Mersenne number about which we don't know the divisors.

is 77-gonal number and an abundant number.

= 444 in base 7.
= 2² x 3 x 19
= 29 + 31 + 37 + 41 + 43 + 47 (sum of consecutive primes)
= 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 (sum of 10 consecutive primes)

is prime, and twin prime with 227.
is also the smallest prime which remains prime when added to its reverse.
is the number of different projective configurations, in which 12 points and 12 lines meet with 3 lines through each of the points and 3 points on each of the lines.

= 4⁴ - 3³

is the number of space groups, describing all possible crystal symmetries.

= 6² + 7² + 8² + 9² (sum of consecutive squares)

is a triangular number: 231 = 1 + 2 + 3 + … + 19 + 20 + 21
is also an hexagonal and an octahedral number.
is the number of partitions of 16.

is exactly the number of cubic inches in an American gallon. The fact that this is exact (by definition) makes it useful for deriving other conversion constants, for instance, that there are 12 x 12 x 12/231 = 7.4805194... gallons in one cubic foot. This removes some of the uncertainties of rounding. -- Charles Gardner, Salford, USA.

= 2² + 3² + 7² + 13² (sum of prime squares)

1/231 = 3/7 - 1/3 - 1/11

is decagonal number.
is the number of 7 by 7 symmetric permutation matrices.

= 2³ x 29
= 2⁴ + 6³ = 2³(2² + 5²) = 2(4² + 10²)

is a Fibonacci prime. If divided by the Fibonacci number 144, it approximates the golden ratio!

233 can be the hypotenuse of a Pythagorean triangle; in fact it is also the smallest 3-digit number such that it and its neighbors (232, 234) can be written as a sum of 2 squares.

= 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 (sum of consecutive primes)

= 2 x 3² x 13
= 3⁵ - 3²
= 3² + 15²
= 2(6² + 9²)

is a centered triangular number (= [3xn² + 3xn + 2] / 2, n = 12).
is the smallest integer whose first two digits are different primes such that their sum equals the 3^rd digit.
is the number of trees with 11 vertices.

= 73 + 79 + 83 (sum of consecutive primes)

235 lunar months made up almost exactly 19 solar years (Metonic cycle: 19 tropical years ≈ 235 synodic months ≈ 6939.6... days )

the product of the digits of 236 is the reverse of the sum of its prime factors:
2 x 3 x 6 = 36 and 2 + 2 + 59 = 63

= 2² x 59
= 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 (sum of first consecutive primes)

is the smallest 3-digit number with its digits being 3 different primes that is not prime nor any of the permutations of its digits represent a prime number.
is the lowest number such that its first 3 multiples contain the digit 7.

'Room 237' plays a relevant role in the Stanley Kubrick film "The Shining".

Researchers count 237 reasons to have sex!

is the largest number that cannot be written as a sum of 8 or fewer cubes:
239 = 5³ + 3 x 3³ + 4 x 2³ + 1³ (= 9 cubes)
239 = 2 x 4³ + 4 x 3³ + 3 x 1³ (= 9 cubes) ... etc.

239² = 2 x 13⁴ - 1

This prime number appears in one of the earliest known geometrically converging formulas for computing :
/4 = 4 arctan(1/5) - arctan(1/239)

is the smallest number with 20 divisors.
n^x - n^x-4 is divisible by 240 if x > 7.

The maximum number of divisors for any integer less than 1,000,000 is 240. Only 5 numbers less than 1,000,000 have 240 divisors: 720720, 831600, 942480, 982800, 997920.

A cholesterol level of 240 and above is considered high risk.

is a prime number.

= (2⁸ + 4⁸ + 1⁸) / (2⁴ + 4⁴ + 1⁴)

is a nontotient, and the smallest number (except 2) that can be written as the sum of 2 squares or the sum of 2 fifth powers.

= 1³ + 3³ + 6³ (sum of cubes)

= ₉C₂ + ₉C₄ + ₉C₆

= 2 x 3 x 41
= 3³ + 3³ + 4³ + 4³ + 4³ (sum of cubes)

= 2⁸ - 2³

is the 5^th central binomial coefficient.

= (10 x 9 x 8 x 7 x 6)/(5 x 4 x 3 x 2 x 1)

252 x 252 = 441 x 144 (palindromic equality)

If you flip a coin 10 times in a row, there are exactly 252 ways in which it can turn out that you get exactly 5 heads and 5 tails.

is the lowest non-trivial triangular star number.

= 1 + 2 + 3 + … + 20 + 21 + 22
= 1⁄2 (22 x 23)
= 4³ + 4³ + 5³

= 11111111 in base 2.

255 x 807 = 205785
(the product has the same digits as its factors)

is the smallest 8^th power (besides 1):
= 2⁸ = 4⁴ = 16²

= 1 0000 0000₂
= 100₁₆

= 2⁹ - 2⁸
= 4³ + 4³ + 4³ + 4³
= 3⁵ + 3² + 3¹ + 3⁰
256 = 2 x 5 + 6

is a Fermat prime.

_{= 2}2³_{+ 1}

= 1⁸ + 2⁸

Most corpses in the wild are skeletonized or mummified according to the formula: y = (257 · 5)/x, where x is the average temperature in Centigrade, and y is the total number of days.

is the constant of a 8x8 magic square.
= 2² x 5 x 13
= (1 + 2 + 3 + … + 62 + 63 + 64) / 8

is the number of days in the "Tzol k'in", the almanac cycle Mayans used for divination.

is is a prime number that is equal to the arithmetic mean of the nearest primes above and below: (269 + 257) / 2

= 43 + 47 + 53 + 59 + 61 (sum of consecutive primes)

seems to be the largest number whose square is 'undulating': 264² = 69696

n¹⁰ - 1 is divisible by 264 if n is prime and n > 3.

= 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 (sum of consecutive primes)

= 2³ + 2³ + 5³ + 5³

In nature, there are 266 different kinds of atoms.

is a deficient number, and the number of planar partitions of 12.

= 1³ + 2³ + 2³ + 5³ + 5³
= 2³ + 2³ + 2³ + 3³ + 6³ (sum of cubes)

seems to be the smallest number whose product of digits is 6 times the sum of its digits.

= 131 + 137 (sum of consecutive primes)

is a prime number, and twin prime with 271.

= 83 + 89 + 97 (sum of consecutive primes)

is a harmonic divisor number.
270 - 1 and 270 + 1 are primes.
10! has 270 divisors.

is a prime and a centered hexagonal number.
is the smallest prime p such that (p - 1) and (p + 1) are both divisible by a cube.

= 10³ - 9³ (difference of cubes)

= 333 in base 9.

is a prime and a Perrin number.

= 3³ + 5³ + 5³ (sum of cubes)
1/2 + 1/3 + 1/5 + 1/7 + 1/11 + ... + 1/271 + 1/277 > 2

is a nontotient.

= 2 x 139

is a prime number.

= 29 + 31 + 37 + 41 + 43 + 47 + 53 (sum of consecutive primes)

is a tetrahedral number.
is the number of rooted trees with 9 vertices.

= C₁₃³ = C₁₃¹⁰

= 7 x 41

seems to be the smallest non-palindrome and non-square that when multiplied by its reverse gives a square:
288 x 882 = 504²

is a square (17²) with non-decreasing digits.

= 1³ + 2³ + 4³ + 6³
= 0⁰ + 1¹ + 2² + 3³ + 4⁴

289 = (8 + 9)²

Radio frequences of 289 kHz are fatal to insects.

is the product of three distinct prime numbers:
= 2 x 5 x 29

= 3 x 97

is a prime number.

= 11 + 101 + 181 (sum of the first 3 tetradic primes)
= 2³ + 2³ + 3³ + 5³ + 5³ (sum of cubes)

= 2 x 3 x 7²

is a self-number.

= 13 x 23

is a happy number, and a 6-hyperperfect number.

= 7 x 43
= 97 + 101 + 103 (sum of consecutive primes)

"I have some eggs in my basket. If I count them in 2s, in 3s, in 4s, in 5s, or in 6s I have always 1 egg left over. But if I count them in 7s there are no remainder. How many eggs are in my basket?" Solution: 301.

is a lucky number.

its cubic power is a concatenation of other cubes:
303³ = 27818127 (27 8 1 8 1 27)

is the difference of the third pair of amicable numbers:
2924 - 2620 = 304

relationships between 304 and 27:
304 = 3 x 10 x 10 + 4 and 27 = 3 + 10 + 10 + 4
304 = 2⁴ x 19 and 27 = 2 x 4 + 19

= 41 + 43 + 47 + 53 + 59 + 61 (sum of consecutive primes)

is the 5^th 'hexagonal prism' number. An hexagonal prism number is of the form (n + 1)(3n² + 3n + 1).

305² = 207² + 224² = 136² + 273² (Pythagorean triple)

= 5 x 61

is a prime, and a non-palindrome having a palindromic square:
307² = 94249

is a Harshad number, and a heptagonal pyramidal number.

= 151 + 157 (sum of consecutive primes)

is a permutable prime.

is a palindromic prime.
is the only 3-digit number being a palindromic prime in base 10 and in base 2 (=100111001) as well. - Larsen
[Editor's note: the next palindromic prime in both base 10 and base 2 is 7284717174827]

= 12² + 13²

3443 / 313 =11
37873 / 313 = 121
(all terms are palindromic!)

10³¹³ + 313 is prime

The reciprocal of 313 (=1/313) produces a string of decimals that repeats itself after 312 (one less than itself) decimals.

is the licence plate number on Donald Duck's car.

represents the number of unlabeled partially ordered sets of 6 elements.

= 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 (sum of consecutive primes)

cannot be represented as the sum of fewer than 19 fourth powers: 3 x 3⁴ + 4 x 2⁴ + 12 x 1⁴
is the smallest number with the property that the partition with the largest product does not have the largest number of parts. -Selfridge

= 103 + 107 + 109 (number of consecutive primes)

is the maximum determinant of a 10 by 10 matrix of zeros and ones.

320!+1 is prime.

= 2⁶ · 5 = 2⁵ · (2·5)

is the 12^th Lucas number.

The emblem of the secret society 'Skull and Bones' consists of a skull and crossbones, along with the number 322. The Order of Skull and Bones is based at Yale University, in New Haven, Connecticut.

is the product of twin primes (twin primes are pairs of primes of the form p, p+2): 323 = 17 x 19

= 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 (sum of consecutive primes)

= 18²
= 73 + 79 + 83 + 89 (sum of consecutive primes)
324 = 3² x 4

324! - 1 is prime...

is a prime number.
= 11² - 10²
= 59 + 61 + 67 + 71 + 73 (sum of consecutive primes)

is the number of 7-hexes.
is a half-evil number: 666/2
represents the millesimal finenes of 8 carat.
= 3² x 37
= 370 - 37

336 x 951 = 319530
(the product has the same digits as its factors)

= 2⁴ x 3 x 7

= ₈P₃

= 6 x 7 x 8

is a permutable prime with 373 and 733.
is a 4-dimensional centered cube prime (primes of the form n⁴+(n+1)⁴ )

_{= 2}2³ _{+ 3}2² _{- Kulsha}

is a value of n for which n!+1 is prime.

= 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 (sum of consecutive primes)
= 4¹ + 4² + 4³ + 4⁴ (sum of powers of 4)
= 12² + 14² = 4² + 18²

is the smallest pseudoprime in base 2.
is a star number.

= 11 x 31
= 37 + 41 + 43 + 47 + 53 + 59 + 61 (sum of consecutive primes)
= 4⁰ + 4¹ + 4² + 4³ + 4⁴ (sum of powers of 4)

= 3 x 5 x 23

is a triangular number and the smallest number n where n, n+1, and n+2 are all products of 4 or more primes.

are the different arrangements of 9 non-attacking Queens on an 9 by 9 chessboard.

= 173 + 179 (sum of consecutive primes)

is the number of degrees in a circle. This size for angular division was chosen by the Babylonians because it is 60²/10 and because it is close to the distance the sun moves through the zodiac each day... In other words, it is close to the length of the tropical year. In n days, the sun moves just about n degrees across the zodiac.

can be evenly factored in 24 different ways — more than any other number of this size.

= 2³ x 3² x 5

= 360 = 3! x 60 (autothecal number)

= 3 x 11²
= 3¹ + 3² + 3³ + 3⁴ + 3⁵
= 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59
(sum of consecutive primes)

363² + 484² = (11 x 55)² (quasi-palindromic pythagorean triples) - G. Sarcone

represents the number of octominoes.

= (1 + 2 + 3 + ... + 79 + 80 + 81) / 9

is a Narcistic or Armstrong number since it equals the sum of the cube of its digits: 3³ + 7³ + 0³

is the average of the  sum of all the possible permutations that we can made with it:
073 + 037 + 307 + 370 + 703 + 730 = 2220
Average: 2220/6= 370
other numbers with this property are: 407, 481, 518, 592, 629 and all repdigit numbes. You can see more examples here.
-- Posted by Claudio Meller

= 83 + 89 + 97 + 101 (sum of consecutive primes)

is an Armstrong number since it equals the sum of the cube of its digits: 3³ + 7³ + 1³

= 7 x 53

= 7 + 11 + 13 + ... + 43 + 47 + 53 (sum of consecutive primes)
= 41 + 43 + 47 + 53 + 59 + 61 + 67 (sum of consecutive primes)

is a hexagonal pyramidal number.

= 2² x 3 x 31

= 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 (sum of consecutive primes)

is a permutable prime.

= 3² + 5² + 7² + 11² + 13² (sum of consecutive square primes)
= 67 + 71 + 73 + 79 + 83 (sum of consecutive primes)

is the smallest number that can be written as the sum of 3 squares in 8 different ways

= 2 x 11 x 17

is a truncated tetrahedral number.
represents the millesimal finenes of 9 carat.

= 3 x 5³

is an automorphic number:
376² = 141376
376³ = 53157376
376⁴ = 19987173376 ...

= 2³ x 47

is a Kaprekar constant in base 2.

381 x 969 = 369189
(the product has the same digits as its factors)

is a palindromic prime number.
is the number of 7-vertex Hamiltonian graphs.

= 101 + 131 + 151 (sum of 3 consecutive palindromic numbers)

= 2⁷ x 3
= 3 x 8 x 4²

= 5 x 7 x 11
is a square pyramidal number because:
1² + 2² + 3² + … + 8² + 9² + 10² = 385
is the number of partitions of 18.

= 193² - 192²

is the 12th term in the sequence involving rooted polygonal cacti (Husimi graphs) with n nodes.

= 193 + 197 (sum of consecutive primes)
= 89 + 97 + 101 + 103 (sum of 4 consecutive primes)

is a Harshad number and a Kaprekar constant in base 5.

= 2³ x 7²

is a value of n for which n!+1 is prime.
is a Harshad number and the smallest Lucas-Carmichael number.

= 7¹ + 7² + 7³
= 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 (sum of consecutive primes)

is a square number.
= 1111 in base 7.
= 7⁰ + 7¹ + 7² + 7³
= 2⁴ x 5²

Just one cow can belch (and fart) enough harmful methane gas in a single day to fill around 400 liter bottles.

= 1³ + 4³ + 5³ + 6³
= 1³ + 2³ + 3³ + 3³ + 7³

406 is a poem by John Boyle O'Reilly.

is a Narcistic or Armstrong number since it equals the sum of the cube of its digits: 4³ + 0³ + 7³

= 11 x 37

is a nontotient, and a stella octangula number.

is a nontotient.
when squared it gives a concatenation of 2 consecutive numbers: 428² = 183 184

= 2² x 107

is a sphenic number, and the 7^th Catalan number.

is a sphenic number.

= 2 x 5 x 43

is a Chen prime.

431/510 = log₁₀7 (exact to the 7th decimal place, the difference is actually 0.00000000798570432...)
= 47 + 53 + 59 + 61 + 67 + 71 + 73 (sum of consecutive primes)

432 + 1 and 432 - 1 are twin primes.

= 4 x 3³ x 2²
= 103 + 107 + 109 + 113 (sum of consecutive primes)
= 12³ - 6⁴ - G. Sarcone
= 12² + 12² + 12²
= 6³ + 6³ - G. Sarcone
= 55 + 144 + 233 (sum of 3 Fibonacci numbers with repeating digits)
= 55 + 377 (sum of 2 Fibonacci numbers with repeating digits) - G. Sarcone

A manufacturer of golf balls once did a test to find the ideal number of dimples to put on golf balls for optimum aerodynamic effect. It turned out that balls with 432 dimples went farther than the rest (United States Patent 5106096).

is equal to 3 'gross'. A gross is a dozen dozen, i.e.: 12 x 12 = 144 (see above)

432 x 10² is an average person’s heartbeats in a day.

Four hundred thirty-two is also a number that is very closely related to many astronomical events. For example, the diameter of the sun is 864,000 miles (432 x 2 x 10³). The diameter of the moon is 2,160 miles (432 x 10 / 2). If these measurements were not as they are, we would not experience a total eclipse of the sun.

is prime, and a star number.

= (13³ - 11³) / 2

is a triangular and a hexagonal number.

= 3 x 5 x 29

is a nontotient.

= 2² x 109

is the sum of the first 17 prime numbers:
= 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59

= 2² x 5 x 11
= 21² - 1²
= 27² - 17²
= 57² - 53²
= 111² - 109² (differences of squares)
= 2³ + 3³ + 4³ + 5³ + 6³ (sum of consecutive cubes)

is the smallest square which is the sum of 6 consecutive cubes: 1³ + 2³ + 3³ + 4³ + 5³ + 6³

= 3² x 7² = 21²
= 29² - 20²
= 35² - 28²
= 75² - 72²
= 221² - 220² (differences of squares)
= ( 1 + 2 + 3 + 4 + 5 + 6)²

is the largest known n for which there is a unique integer solution to a₁+...+a_n= (a₁)...(a_n).

= CDXLIV in late roman numeration system

is the smallest number that can be written as the sum of 3 distinct squares in 8 ways.

= 9² + 10² + 11² + 12²

is the sum of two consecutive primes:
223 + 227

= (5 + 4)(5 + 5)(5 + 0)
= 3² + 21²

= ₁₅C₃

is the number of tournaments with 7 vertices.
is the sum of a twin prime: 227 + 229
is the sum of four consecutive primes:
107 + 109 + 113 + 127

= 456 = 4(5! - 6) (autothecal number)

= 2⁴ x 29

464² + 777² = (5 x 181)² (quasi-palindromic pythagorean triples) - G. Sarcone

is a triangular number.
is a Kaprekar constant in base 2.
= 3 x 5 x 31

465 x 831 = 386415
(the product has the same digits as its factors)

494 + 209 = 703 and 494,209 = 703²
moreover 297+703 = 1000

is the Kaprekar constant for 3-digit numbers.

is the difference of two of its own anagrams:
495 = 954 - 459
(other interesting examples:1089 = 9108 - 8019; 1269 = 2961 - 1692; 2538 = 5823 - 3285...). More examples here.
-- Posted by Claudio Meller

= 3² x 5 x 11

is a triangular number (= 1 + 2 + … + 30 + 31).
is the 3^rd perfect number, that is, a number equal to the sum of all of its proper divisors, 1 included. The formula for finding perfect numbers is: (2ⁿ - 1) x 2^n-1.

= 16 x 31
= 1³ + 3³ + 5³ + 7³

is the number of graphs with 8 edges.

= 7 x 71
= 89 + 97 + 101 + 103 + 107 (sum of consecutive primes)

is a prime number and the smallest number with the property that its first 12 multiples contain the digit 9.

497 + 2 = 499, inversing the number -> 994 = 497 x 2
499³ = 124251499

= 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 (sum of consecutive primes)

is an heptagonal number and a member of the Padovan sequence, coming after 265, 351, 465 (it is the sum of the first two of these).

= 2³ x 7 x 11
= (9² + 10² + 11² + 12² + 13²) + 1 (sum of consecutive squares incremented by 1)

For centuries, people have been intrigued by the number 666 (see '666' further below)... However, researchers are re-examining evidence that the 'Number of the Beast' is not 666 as widely believed, but 616.

Fragment from "Book of Revelation" mentions 616 in the third line – χ khi, ι iota, ς sigma (= 616 in greek numeral notation).

is said to be the occult 'Number of the Beast', aka the 'Sign of the Devil', associated in the Bible with the Antichrist.

lists in their proper order the letters used for numbers in Roman numeration system, namely D (500) + C (100) + L (50) + X (10) + V (5) + I (1), or DCLXVI.

is the largest triangular number that is also a repdigit.
is a palindromic triangular number.
is the sum of the squares of two consecutive triangular numbers: 15² + 21²
is the sum of the squares of the first 7 primes:
2² + 3² + 5² + 7² + 11² + 13² + 17²
is the sum of two consecutive palindromic primes:
666 = 313 + 353
is a divisor of 123456789 + 987654321

= 1234 – 567 + 8 – 9
= 123 + 456 + 78 + 9
(in the equalities above digits 1 through 9 were used once)

There are exactly six 6's in 666⁶. (There are also exactly six 6's in the previous sentence!)

= 18691113009329 - 18691113008663 (difference of 2 consecutive prime numbers)
= 1⁶ - 2⁶ + 3⁶
= 6 + 6 + 6 + 6³ + 6³ + 6³
= 1³ + 2³ + 3³ + 4³ + 5³ + 6³ + 5³ + 4³ + 3³ + 2³ + 1³
= 3(6³ + 6)
= 2 x 3² x 37

The first 2 beasty palindromic primes are:
16661,
1000000000000066600000000000001,
can you find the next one?

-2sin(666) =
sin(666) = cos(6 x 6 x 6)

If we split 1010011010 - the binary notation for 666 - into two digits sets (10100 and 11010), the second part of the number is the complemented reverse of the first part:
10100 00101 (00101 reverse of 10100)
10100 11010 (11010 complement of 00101)
- By G. Sarcone -

Tuesday, 6 June 2006 is 06-06-06; this convergence of three sixes being the Mark of the Beast, some people believe that it is the 'Apocalypse day'. But if you read this, it means that the End of the World has been postponed until June 2066!

Take ANY number having 3 consecutive digits and sum all 6 possible combinations, here 789:
789 + 798 + 879 + 897 + 978 + 987 = 5,328
Now, if your divide the result by 8 you'll obtain 666.

The number 666 can also be found in a number of words and phrases. For example, summing the ASCII character codes for INDONESIA gives 666.

Strangely, the number 666 is a good omen (lucky number) for ethnic Chinese couples marrying in Malaysia. Actually, in Hokkien dialect, the number '6' is pronounced as "luck". Thus, many Chinese believe that tying the knot on June 6th, 2006 that appears as 060606 on the marriage certificates can only triple the luck for the newly-weds.

Contrary to popular myth, no bar code includes the number 666. This belief arose because the number 6 is represented by a pattern similar to that of the 'guard bars' used to mark the beginning, middle, and end of every bar code (the guard bars indicate the computer-scanner when the product code begins and ends). Since the guard bars always appear three times in a given bar code, people who mistakenly read them as 6s claimed that the pattern 6-6-6 was embedded in every bar code. However, looking closely at the '6' in a bar code, we can see that there is a wide white bar either to the left or the right of its pattern, which is not the case with the guard bars. The only numbers on the bar code which are scanned are those shown in the conventional numerals underneath it.

References from the Bible:

In the King James Version, excerpt from 'Revelation 13:18':

Here is wisdom: let him who hath understanding count the number of the beast: for it is the number of a man; and his number is 'six hundred three score and six'.

This calls for wisdom. Whoever is intelligent can figure out the meaning of the number of the beast, because the number stands for the name of someone. Its number is '666'.

Ὧδε ἡ σοφία ἐστίν· ὁ ἔχων νοῦν ψηφισάτω τὸν ἀριθμὸν τοῦ θηρίου, ἀριθμὸς γὰρ ἀνθρώπου ἐστίν· καὶ ὁ ἀριθμὸς αὐτοῦ ἑξακόσιοι ἑξήκοντα ἕξ.

(Hōde hē sophia estin; ho echōn noun psēphisatō ton arithmon tou thēriou, arithmos gar anthrōpou estin; kai ho arithmos autou 'hexakosioi hexēkonta hex')

Other manuscripts use the numerical form χξς´ (see number 616 above).

The Vulgate also mentions the 'Number of the Beast':

Hic sapientia est. Qui habet intellectum, computet numerum bestiae. Numerus enim hominis est, et numerus eius est 'sescenti sexaginta sex'.

The fear of the number 666 is called hexakosioihexekontahexaphobia.

Mansinthe, a new absinthe liquor dedicated to the rock singer Marilyn Manson has 66.6% alcoholic content per volume.

Buy your favorite Number (666) here .

seems to be the first uninteresting number. But since it is the least uninteresting number it becomes, ipso facto, interesting. Suppose we've divided the numbers into 2 sets: interesting and not interesting. We must therefore remove 684 from the uninteresting numbers set and place it in the interesting numbers set. But now, there will be another smallest uninteresting number. Repeating this process will make any common number interesting. In conclusion... There are no uninteresting numbers! (This conclusion contradicts the intuitive notion that the natural numbers are apparently too many for all of them to be subjectively interesting)

is a pentatope number.

715 x 31237 (a prime) = 22334455

= ₁₃C₄

Brazillion is a very large number; indescribable by regular numeralogical values such a million or billion.

Joke: The Secretary of Defense is giving President Bush his daily briefing. He concludes by saying: "Yesterday, three Brazilian soldiers were killed".
" Oh, no!" the President exclaims. "That's terrible!"
His staff sits stunned at this display of emotion, nervously watching as the President sits, head in hands.
Finally, the President looks up and asks, "How many is a brazillion?"

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Encyclopedia of Numbers © G. Sarcone, Archimedes Lab, Genoa, Italy