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Zoo of Numbers: Numbers 201 to 684

 
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Books by the same authors of Archimedes Lab Project
Eye bogglers
EYE BOGGLERS, ISBN 1780970749
Curiopticals
CURIOPTICALS, ISBN 1847322298
3D Optical Illusions
3D ILLUSIONS, ISBN 1780970056
World of Optical Illusions
WORLD OF ILLUSIONS, ISBN 1848586647
Drawing Optical Illusions
DRAWING OPTICAL ILLUSIONS, ISBN 1848378203
Optical Puzzles
OPTICAL PUZZLES, ISBN 1848589395
Amazing Visual Illusions
AMAZING ILLUSIONS, ISBN 1848378300
Prestidi-Geometrie
PLIAGES, DECOUPAGES, MAGIE, ISBN 2848841656
Etrange Univers des Illusions d'Optique
L'UNIVERS DES ILLUSIONS, ISBN 2215110120
MateMagica
MATEMAGICA, ISBN 1780970056
FantaLogica
FANTALOGICA, ISBN 1780970056
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201

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

202 = 2 x 101
= (2 + 3 + 5 + 7)2 - (22 + 32 + 52 + 72) - Trotter & De Geest
= 43 + 47 + 53 + 59 (sum of 4 consecutive primes)
202 x 11 = 2222
203

is the sixth Bell number.

2032 + 2030 + 2033 is prime.
204

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)
= 20 + 19 + 18 + ... + 6 + 5 + 4 (reverse sum of consecutive integers in the number) -- Matthew Goers
= 23 + 29 + 31 + 37 + 41 + 43 (sum of consecutive primes)

= 22 x 3 x 17

2042 = 233 + 243 + 253

205

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)

206

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)

207

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).

208

is a tetranacci number.
is a divisor of 252 - 1

= 24 x 13
= 82 + 122
= 28 - 48
= 22 + 32 + 52 + 72 + 112 - Sladcik
= 23 + 23 + 43 + 43 + 43

209

is a Harshad number and the smallest quasi-Carmichael number in base 9.
is the smallest number with 6 representations as a sum of 3 squares: 209 = 12 + 82 + 122 = 22 + 32 + 142 = 22 + 62 + 132 = 32 + 102 + 102 = 42 + 72 + 122 = 82 + 82 + 92

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

210 is the product of the first 4 primes:
= 2 x 3 x 5 x 7
is a triangular number.
= 1 + 2 + 3 + 4 + ... + 17 + 18 + 19 + 20
211

is a Chen prime.

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

212

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)

= 22 x 53
213 = 3 x 71
= 23 + 23 + 23 + 43 + 53
214 is the number of bones in a human skeleton.
is the number of Chinese radicals (main characters) essential for locating words in Chinese dictionaries.
= 2 x 107
= 23 + 33 + 33 + 33 + 53
215

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

216

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

= 21 + 20 + 19 + ... + 8 + 7 + 6 (reverse sum of consecutive integers in the number) -- Matthew Goers

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

12 1 18
9 6 4
2 36 3
217

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)
= 93 - 83 (difference of consecutive cubes)

218

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

= 72 + 132 (sum of squares) - Walter Seaman
= 73 - 53 (difference of cubes)

219

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

= 33 + 43 + 43 + 43

220

is the smallest amicable number.

= 47 + 53 + 59 + 61 (sum of consecutive primes)
221

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

222 is the number of lattices on 10 unlabeled nodes.
= 2 x 3 x 37
= 109 + 113 (sum of consecutive primes)
223

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

224 = 25 x 7
= 23 + 33 + 43 + 53 (sum of consecutive cubes)
= 28 - 25
225

is an octagonal square number.

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

226

is a centered pentagonal number.

= 2 x 113
= 2(72 + 82)

227

road numberis 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.

228

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)

229

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.

= 126(2/6 + 3/7 + 4/8 + 5/9)
= 44 - 33

230

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

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

231

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

232

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

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

233

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)

234

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

235

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 3rd 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 )

236

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)

237

number 237is 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!

238 = 2 x 7 x 17
= 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 (sum of the first 13 primes)
239

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 Pi:
Pi/4 = 4 arctan(1/5) - arctan(1/239)

240

is the smallest number with 20 divisors.
nx - nx-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.

241

is a prime number.

= (15 + 4i)(15 - 4i)
= (28 + 48 + 18) / (24 + 44 + 14)

can be represented as:
241 = 42 + 152 = 32 + 62 + 142 = 62 + 62 + 132
is the sum of 170 and its reverse:
241 = 170 + 071

2412 = 292812 + 501602
2412 = 290412 - 290402 (Pythagorean triples)

242 is the smallest number n where n through n+3 are all products of 3 or more primes.
= 11 x 22
= 59 + 60 + 61 + 62
= 44 + 55 + 66 + 77
243 is the sum of five consecutive primes:
41 + 43 + 47 + 53 + 59
= 35
= 100 000 in base 3
1 / 243 = 0.004115226337448559...
244

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)

245 is a stella octangula number.
= 5 x 72
= 82 + 92 + 102 (sum of consecutive squares)
246

= 9C2 + 9C4 + 9C6

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

247 is the smallest possible difference between 2 integers that together contain each digit exactly once.
its digits sum to its smallest prime factor:
247 = 13 x 19 and 2 + 4 + 7 = 13
248

= 28 - 23

249 = 3 x 83
250 = 2 x 53
251 is the smallest number that can be written as the sum of 3 cubes in 2 ways:
= 23 + 33 + 63 = 13 + 53 + 53
252

is the 5th 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.

253

is the lowest non-trivial triangular star number.

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

254 = 28 - 21
255

= 11111111 in base 2.

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

256

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

= 1 0000 00002
= 10016

= 29 - 28
= 43 + 43 + 43 + 43
= 35 + 32 + 31 + 30
square root256 = 2 x 5 + 6

257

is a Fermat prime.

= 223+ 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.

258 = 2 x 3 x 43
= 61 + 62 + 63
= 59 + 61 + 67 + 71 (sum of consecutive primes)
259 = 1111 in base 6.
= 13 + 23 + 53 + 53
= 23 + 23 + 33 + 63
260

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.

are the pounds of oxygen that one tree can produce each year.

261 is the number of different ways to dissect a 16-gon into 7 quadrilaterals.
262 is the 9th meandric number.
263

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)

264

is an integer n such that n2 + 1 is a prime: 2642 + 1 = 69697
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.

= 25 + 63 + 42
= 23 + 43 + 43 + 43 + 43 (sum of five cubes)
= 172 - 52 (difference of squares)

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

Sleep deprivation record: 264 is the longest documented number of hours a person has gone without sleep.

265

is a Padovan number and a centered square number.
is the hypotenuse of two Pythagorean triples:
2652 = 232 + 2642 = 962 + 2472
is the number of derangements of 6 items.

= 112 + 122 (sum of consecutive squares)
= 32 + 162

= !6 = 6!(1 - 1/1! + 1/2! - 1/3! + 1/4! - 1/5! + 1/6!)

266

is a divisor of 113 - 1.

= 23 + 23 + 53 + 53 (sum of four cubes)

Mathematically correct result derived by incorrect calculation method (anomalous cancellation):
266 = 266 = 2
665    665   5

In nature, there are 266 different kinds of atoms.

The gestation period for humans is about 266 days.

267

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)

268

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

= 131 + 137 (sum of consecutive primes)

269

is a prime number, and twin prime with 271.

= 83 + 89 + 97 = 131 + 137 (sum of consecutive primes)

The 269th day of a non-leap year is 26 September (26/9).
-- Claudio Melle
r

270

is a harmonic divisor number.
is the smallest positive integer that has divisors ending by digits 1, 2, 3, …, 7, 8, 9.
is a number n such that 6n - 1 and 6n + 1 are twin primes: 6x270 - 1 = 1619 and 6x270 + 1 = 1621

270 - 1 and 270 + 1 are primes.
2702 + 1 is prime.
10! has 270 divisors.

= 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 (sum of consecutive primes)
= 33 + 33 + 63 (sum of cubes)

sin270° = cos180° = tan135° = –1
cos270° = sin180° = tan180° = cot90° =
= cot270° = 0

According to Worldwatch, 270 thousand trees are flushed down the toilet or end up as garbage every day around the world (data 2010).

Owl headOwls are able to rotate their head a full 270° to compensate for their ocular immobility.

271

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)

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

272 is the 7th Euler number.
= 16 x 17 = 172 - 171
= 61 + 67 + 71 + 73 (sum of consecutive primes)
273

= 333 in base 9.
= 111 in base 6.

-273.15 °C is the lowest temperature theoretically obtainable (absolute zero).

273 seconds was the duration of the silent symphony 4'33'' by John Cage. The piece consists of the pianist going to the piano, and not hitting any keys for four minutes and thirty-three seconds. In other words, the entire piece consists of silences!

274 is a tribonacci number: 44 + 81 + 149
sum of cubes: 23 + 23 + 23 + 53 + 53
275 = 52 x 11
276 is the sum of the first three 5th powers:
= 15 + 25 + 35
277

is a prime and a Perrin number.

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

278

is a nontotient.

= 2 x 139

279 is the smallest number whose product of digits is 7 times the sum of its digits.
280 is an octagonal number.
= 23 x 5 x 7
281

is a prime number.

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

282 is the sum of its proper divisors containing the digit 4:
47 + 94 + 141
is the smallest multi-digit palindrome sandwiched between twin primes: 281 and 283.
283 is a prime number.
= 25 + 8 + 35
284 is an amicable number (with 220).
= 22 x 71
285 = 12 + 22 + 32 + … + 72 + 82 + 92 (sum of consecutive squares)
286

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

= C133 = C1310

287

= 7 x 41

= 89 + 97 + 101
= 47 + 53 + 59 + 61 + 67
= 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 (sums of consecutive primes)
288

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

= 4! x 3! x 2! x 1!
289

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.

290

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

= 67 + 71 + 73 + 79 (sum of consecutive prime numbers)
291

= 3 x 97

292 is the number of ways to make change for 1 dollar (or for 1 Euro, with 1, 5 and 25 cents).
293

is a prime number.

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

294

= 2 x 3 x 72

111152 - 2942 = 123,456,789
295 = 5 x 59
296 = 23 x 37
297 is a Kaprekar number:
2972 = 88 209; 297 = 88 + 209
298 = 2 x 149
299

is the smallest number whose sum of digits is 20.
is a self-number.

= 13 x 23

is the maximum number of pieces into which a 3-dimensional space can be cut with a given number of plane cuts: a sphere sliced with 12 straight cuts produces 299 pieces.

300

is a triangular number, that is the sum of all positive integers up to 24.
is the largest possible score in bowling.

= 22 x 3 x 52

= 149 + 151 (sum of twin primes)
= 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 (sum of consecutive primes)

300 m/s is the speed of the sound in the air.

Different late Roman notations of number 300:
CCC, or XVxx, or IIIc.

All human beings are born with 300 bones, but adults only have 206 because some fuse together naturally.

The Spartan king Leonidas led an extremely small army of 300 Greek Soldiers to hold off an invading Persian army more than 20 times as large. The "Three Hundred" (οι τριακόσιοι) was the name given to those Spartans who fought to the death at the Battle of Thermopylae.

Habanero chili"Scovilles" are the number of units of water needed to render a unit of pepper ‘untingly’ to the human tongue. For instance, habaneros are the hottest chili peppers and rate around 200,000 - 350,000 Scoville units; that is, 1 cc of habanero chili after being diluted in 300 liters of water still gives the feeling of hotness!

301

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.

302 = 92 + 102 + 112 (sum of consecutive squares)
303

is a lucky number.

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

A Centillion has 303 zeros and is the highest number recognized by orthodox mathematics... Any number higher than a Centillion is considered an unimaginable abstraction belonging to the realm of infinity.
304

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)

305

is the 5th '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

306 = 2 x 32 x 17
= 71 + 73 + 79 + 83 (sum of consecutive primes)
307

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

= 13 + 53 + 33 (sum of cubes)
308

is a Harshad number, and a heptagonal pyramidal number.

= 151 + 157 (sum of consecutive primes)

311

is a permutable prime.

Four distinct sums of consecutive primes:
= 101 + 103 + 107
= 53 + 59 + 61 + 67 + 71
= 31 + 37 + 41 + 43 + 47 + 53 + 59
= 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47

The 11th letter of the alphabet is the letter 'K'; thus 3 times 11 equals 'KKK', or Ku Klux Klan. 311 is sometimes used as a greeting to demonstrate membership in the KKK or simply sympathy with the Klan and its ideology. There is also a popular rock band with the name "311" which is not at all hate-oriented.

312

= 23 x 3 x 13
= 2222 in base 5.

3122 = 143 + 153 + 163 + 173 + 183 + 193 + 203 + 213 + 223 + 233 + 243 + 253

313

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!)

3132 = 252 + 3122 (Pytagorean triple)

10313 + 313 is prime

The probability that at least five of 313 people will share the same birthday is greater than 50%.

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.

A study carried out in hotels, restaurants, banks, offices and airports found 313 colony forming units of bacteria on every square centimeter of lift button. An elevator buttons is actually 40 times dirtier than toilet seats!

315 = 32 x 5 x 7
= (4 + 3)(4 + 1)(4 + 5)
= (10 - 3)(10 - 1)(10 - 5)
= 7! / 42
= 8! / 27
317 is a prime number.
The number made with three hundred and seventeen 1's is a repunit prime.
317 x 461 = 146137
(the product has the same digits as its factors)
318

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)

319

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)

320

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

320!+1 is prime.

= 26 · 5 = 25 · (2·5)

322

is the 12th Lucas number.

Skull and Bones logoThe 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.
323

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)

324

= 182
= 73 + 79 + 83 + 89 (sum of consecutive primes)
square root324 = 32 x square root4

324! - 1 is prime...

325 is a 3-hyperperfect number.
= 12 + 182
= 62 + 172
= 102 + 152
= 52 x 13
326 = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 (sum of consecutive primes)
327 1 x 327 = 327
2 x 327 = 654
3 x 327 = 981 (the 3 results contain every digit from 1 to 9 exactly once)
330 = 2 x 3 x 5 x 11
= 43 + 47 + 53 + 59 + 61 + 67 (sum of consecutive primes)
= 62 + 72 + 82 + 92 + 102 (sum of consecutive squares)
= 11C4
331

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

333

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

Number patterns:
166,500,333 = 1663 + 5003 + 3333
333,667,000 = 3333 + 6673 + 0003
333,667,001 = 3333 + 6673 + 0013

335 is divisible by the number of primes below it.
336

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

= 24 x 3 x 7

= 8P3

= 6 x 7 x 8

337

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

= 223 + 322 - Kulsha

338 = 2 x 132
339 = 3 x 113
Minuscule 339, is a Greek minuscule manuscript. This codex contains a complete text of the New Testament on 200 parchment leaves (21.6 x 15.7 cm). It is written in two columns per page, in 56-58 lines per page.
340

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

= 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 (sum of 10 consecutive primes)
= 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 (sum of 8 consecutive primes)
= 41 + 42 + 43 + 44 (sum of powers of 4)
= 122 + 142 = 42 + 182

341

is the smallest pseudoprime in base 2. In fact, 341 "fools" the primality test for base 2 because it gives the same result a prime number would: 2(341-1) is 1 modulo 341.
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)

342 = = 2 x 32 x 19
= 666 in base 7.
= 18 x 19
= 13 + 53 + 63 = 73 - 13
343 = 343 = (3 + 4)3 (autothecal number)
= 180 + 181 + 182
344 is an octahedral number: 8(2 x 82 + 1)/3
= 23 x 43
= 43 + 43 + 63 = 13 + 73
345

is the average number of squirts from a cow's udder needed to yeld a US gallon of milk.

= 3 x 5 x 23

346 is a Smith number.
= 2 x 173
347 is a prime number.
= 347 = 4 + 73
348 = 22 x 3 x 29
= 79 + 83 + 89 + 97 (sum of consecutive primes)
349 is a prime number.
= 109 + 113 + 127 (sum of consecutive primes)
350 = 2 x 52 x 7
351

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

= 33 x 13
= 61 + 67 + 71 + 73 + 79 (sum of consecutive primes)
352

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

= 22 x 11
= 173 + 179 (sum of consecutive primes)

353

is the smallest number whose 4th power can be written as the sum of four 4th powers:
3534 = 304 + 1204 + 2724 + 3154


= 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 (sum of consecutive primes)
354 = 14 + 24 + 34 + 44 (sum of the first four 4th powers)
= 354 = 3(5! - root4) (autothecal number)
355 is the number of labeled topologies with 4 elements.
= 355 = 3 x 5! - 5 (autothecal number)
360

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)

361 is the number of possible positions on a Go board.
= 19 x 19
362 = 2 x 181 = 2 x (92 + 102)
363

= 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

364 is a tetrahedral number.
= 12 x 13 x 14/6
= 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53
(sum of consecutive primes)
= 14C3 = 14C11 (Pascal's triangle number)
365 is the number of the days in a year.
is the smallest number that can be written as a sum of consecutive squares in more than 1 way:
= 102 + 112 + 122 = 132 + 142
366 is the number of days in a leap year.
= 82 + 92 + 102+ 112
367 is known as the largest number whose square has strictly increasing digits: 3672 = 134689
369

represents the number of octominoes.

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

370

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)

371

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)

372

is a hexagonal pyramidal number.

= 22 x 3 x 31

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

373

is a permutable prime.

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

374

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

= 2 x 11 x 17

375

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

= 3 x 53

376

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

= 23 x 47

377 is the 14th Fibonacci number.
381

is a Kaprekar constant in base 2.

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

383

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

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

384

= 27 x 3
= 3 x 8 x 42

= 53 + 59 + 61 + 67 + 71 + 73 (sum of consecutive primes)
385

= 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

386 is a nonagonal and a centered heptagonal number.
390

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)

391 is a centered pentagonal number.
392

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

= 23 x 72

399

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)

400

is a square number. The sum of the divisors of 400 is also a square: 961 = 312
= 1111 in base 7.
= 70 + 71 + 72 + 73
= 70 + 71 + 72 + 180 + 181 + 182
= 122 + 162 (sum of 2 squares)
= 522 - 482 (difference of 2 squares)
= 24 x 52
= 1 + 3 + 5 + … + 35 + 37 + 39 (sum of consecutive odd numbers)

400 is the number of years in the repeating cycle of leap/non-leap years.
400 is the smallest integral number of years that contains an integral number of days, 146,097. (See rules for leap years in the entry for 29) -- Bob Morris

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

401 is the number of connected planar Eulerian graphs with 9 vertices.
= 72 + 82 + 122 + 122
402 = 33 + 53 + 53 + 53
= 2 x 3 x 67
403 = 23 + 33 + 33 + 53 + 63
= 13 x 31
405 is a pentagonal pyramidal number.
= 43 + 53 + 63
= 34 + 34 + 34 + 34 + 34
406

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

406 is a poem by John Boyle O'Reilly.

407

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

= 11 x 37

410

is a sphenic number, that is a positive number which is the product of three distinct prime numbers: 2 x 5 x 41
is the smallest number that can be expressed as the sum of 2 distinct primes in 2 ways: 199 + 211 and 97 + 313

= 72 + 192 = 112 + 172

= 59 + 61 + 67 + 71 + 73 + 79 (sum of consecutive primes)

412

cannot be written as a sum of 3 squares.

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

The Dead Sea, located in the heart of the Rift Valley depression, is the lowest sea on earth and at 412 meters below sea level.
415 = 72 + 82 + 92 + 102 + 112 (sum of consecutive squares)
= (45 + 15 + 55) / (4 + 1 + 5)
416

416,768 = 76824162

is the nickname for Toronto.
417 represents the millesimal finenes of 10 carat.
419

is a twin prime number.
is the smallest number which, when divided by 2, 3, 4, 5, 6 and 7, leaves remainders of 1, 2, 3, 4, 5 and 6 respectively.
is also a Sophie Germain prime because 2 x 419 + 1 = 839 is prime. In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime.

is a divisor of 1311 - 1

419 scam (aka Nigerian advance fee fraud) is a type of fraud named after the article of the Nigerian criminal code under which it is prosecuted.

420

is the smallest integer divisible by 1 through 7.
is the sum of four consecutive primes:
101 + 103 + 107 + 109

= 20 x 21

420, 4:20 or 4/20 refers to consumption of cannabis and, by extension, a way to identify oneself with cannabis subculture. The date April 20 is sometimes referred to as "Weed Day" or "Pot Day".

Section 420 of the Indian Penal Code (also used in Pakistan, Bangladesh and Afghanistan) has become a slang reference for a con-artist or confidence trickster.

421 is a twin prime number and a centered square number.
is the name of a French dice game ('Quatre-cent-vingt-et-un').
= 111 in base 20
= 142 + 152 (sum of 2 consecutive squares)
= 73 + 79 + 83 + 89 + 97 (sum of 5 consecutive primes)
423 = 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 (sum of 13 consecutive primes!)
424 = 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 (sum of 10 consecutive primes!)
425 = 52 x 17
= 82 + 192
= 132 + 162
= 52 + 202
= 137 + 139 + 149 (sum of 3 consecutive primes)
426

is a nontotient, and a stella octangula number.

= 2 x 3 x 71
427 is a value of n for which n!+1 is prime.
428

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

= 22 x 107

429

is a sphenic number, and the 7th Catalan number.
is a divisor of 1003 - 1

= 3 x 11 x 13
= 4 + 5 + 6 + … + 27 + 28 + 29 (sum of consecutive numbers) - Matt Goers

The sum of the 4th powers of the factors of 429 is a prime:
34 + 114 + 134 = 43283

430

is a sphenic number.

= 2 x 5 x 43

431

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

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

golf ballA 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.

433

is prime, and a star number.

= (133 - 113) / 2

434 = 33 + 43 + 73 (sum of cubes)
= 112 + 122 + 132 (sum of consecutive squares)
= 61 + 67 + 71 + 73 + 79 + 83 (sum of consecutive primes)
435

is a triangular and a hexagonal number.

= 3 x 5 x 29

436

is a nontotient.

= 22 x 109

437 = 19 x 23
438 = 666 in base 8.
= 2 x 3 x 73
439 is a prime number.
sum of three consecutive primes:139 + 149 + 151
is the sum of nine consecutive primes:
31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67
440

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)

441

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

442 is the number of planar partitions of 13.
is the sum of eight consecutive primes:
41 + 43 + 47 + 53 + 59 + 61 + 67 + 71
443 is the first 3-digit non-palindromic prime whose binary equivalent is a palindromic prime: 110111011
444

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

= CDXLIV in late roman numeration system

446

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

= 92 + 102 + 112 + 122

448 is the number of 10-iamonds.
= 26 x 7
450

is the sum of two consecutive primes:
223 + 227

= (5 + 4)(5 + 5)(5 + 0)
= 32 + 212

454 is the largest number known that cannot be written as a sum of 7 or fewer cubes.
455

= 15C3

is a tetrahedral number: (13 x 14 x 15)/6
= 5 x 7 x 13
456

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)

457 is the sum of three consecutive primes:
149 + 151 + 157
459 = 33 x 17
954 - 459 = 495
461 is a prime number.
= 444 + 6 + 11
462 is the sum of six consecutive primes:
67 + 71 + 73 + 79 + 83 + 89
= 2 x 3 x 7 x 11
= 11C5
463 is a prime number.
is the sum of seven consecutive primes:
53 + 59 + 61 + 67 + 71 + 73 + 79
464

= 24 x 29

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

465

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)

468 = 3333 in base 5.
= 22 x 32 x 13
is the sum of ten consecutive primes:
29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67
469 is the largest known value of n for which n!-1 is prime.
= 7 x 67
471 is the smallest number with the property that its first 4 multiples contain the digit 4.
480 is the smallest number which can be written as the difference of 2 squares in 8 ways.
n8 – 1 is divisible by 480 if n is prime and n > 5
n9– 1 is divisible by 480 if n is odd and n > 1
481 = 152 + 162 (sum of 2 consecutive integers)
483 is the last 3-digit string in the decimal expansion of .
484 is a palindromic square number.
= 222
= 22 x 112
487 is the number of Hadamard matrices of order 28.
489 is an octahedral number.
490 is the number of partitions of 19.
= 2 x 5 x 72
494

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

= 2 x 13 x 19
495

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

496

is a triangular number (= 1 + 2 + … + 30 + 31).
is the 3rd 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 2n-1.

= 16 x 31
= 13 + 33 + 53 + 73

497

is the number of graphs with 8 edges.

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

499

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)

500
D
D is the symbol for 500 in the Latin numeral system.
"Cinquecento" (500, in Italian) is the name of a small well-known car appreciated worldwide by car enthusiasts.
= 22 x 53
500 : 499 = 1.002004008016032064...
613

is a prime number and centered square number with 18 per side.

There are 613 commandments (Hebrew: תרי"ג מצוות‎: taryag mitzvot, "613 Mitzvot") listed in the Jewish Torah.

The number 613 is a math enigma in the bewildering story 'Number of the End' by Jason Earls:"bring the first digit back to get 136, it's triangular. Now bring the first digit of that back to get 361, it's a square".

= 172 + 182 (sum of 2 consecutive squares)

6132 = 352 + 6122 (Pythagorean triplet)

616

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.

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

625

is a centered octagonal number.
is the hypotenuse of a Pythagorean triple:
6252 = 3362 + 5272
is an automorphic number:
6252 = 390625
6253 = 244140625
6254 = 152587890625...
List of automorphic numbers: 0, 1, 5, 6, 25, 76, 376, 625, 9376, 90625, 109376, 890625, 2890625, 7109376, 12890625, 87109376, 212890625, 787109376, 1787109376, 8212890625, 18212890625, 81787109376, 918212890625, 9918212890625, 40081787109376, 59918212890625...

is the smallest fourth power being the sum of 5 other fourth powers: 54 = 24 + 24 + 34 + 44 + 44

= 73 + 79 + 83 + 89 + 97 + 101 + 103 (sum of consecutive primes)

= 54
= 252
= 72 + 242 (solution of a2 + b2 = z4)
= 152 + 202 (solution of a2 + b2 = z4)

6252 + 1 2502 = 1253
6253 + 1 2503 = 46,8752

2 fourth powers share the same digits:
54 = 625 and 44 = 256

648
64 x 8
64 / 8
64 + 8
64 - 8
=
=

=

=
512 +
8 +
72 +
56 =
----------------
648  
----------------

648 = 162 - 172 + 182 + ... + 302 - 312 + 322 =
= -332 + 342 - 352 + ... + 462 - 472 + 48
2

648 = 832 - 792, where 83 and 79 are consecutive primes (A090785).
648 = 101 + 547, where 101 = prime(26) and 547 = prime(prime(26)).
648 / (6+4+8) is a square (36).
648 divides 536 – 1; also: 2 x 648 - 1 and 2 x 648 + 1 divide 2648 - 1 (see A233089).

648 is also:
• an Abundant number (A005101) because:
σ (648) – 2x648 = 519 > 0.
• an Odious number (A000069) because its binary expansion is 1010001000, which has an odd number of 1's.
• a Smith number (A006753) because 6+4+8 = 2+2+2+3+3+3+3+3 = 18 (being 648 = 23 x 34).
• a Practical number (A005153) because all the numbers from 1 to 647 can be expressed as sums of their proper divisors 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324. For example: 1, 2, 3, 4, 5=1+4, 6=2+4, 7=3+4, 8, 9, 10=1+9, 11=2+9, 12, 13=1+12, 14=2+12, 15=3+12, etc.
• a Powerful number (A001694) because 2 and 22 divide 648; also: 3 and 32 divide 648.

Moreover:
6481/6 = 2.941682753... (first 9 decimal digits - 941682753 - are the integers from 1 to 9).

Number facts above, contributor: Bruno Berselli (from https://oeis.org/)

648 = 12 x 23 x 34

648 = 182 + 182 = 63 + 63 + 63

666

666is 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

1666
6664

= 16
66
x 66
64

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

-2sin(666) = phi
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 -

The number (10666)! is called "Leviathan number", because this incalculable number has approximately 6.656x10668 decimal digits. The number of trailing zeroes in the Leviathan number is 25x10664-143. - C. Pickover

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'.
In the Good News Bible, the same verse reads:
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'.
The Greek text of Codex Alexandrinus of the New Testament runs:
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'.

MansyntheThe 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 buy numbers .

684

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)

715

is a pentatope number.

715 x 31237 (a prime) = 22334455

= 13C4

729

is a centered octagonal number (of the form 4n2 - 4n + 1).
is the smallest odd cube represented as the sum of 2 primes: 729 = 2 + 727

= 36 = 93 = 272 (perfect 6th power)
= 452 - 362 (difference of squares)
= 13 + 63 + 83 (sum of cubes)
= 1 + 3 + 5 + … + 43 + 47 + 53 (sum of consecutive odd primes)

786

50 can be partitioned into powers of two in 786 different ways.

= 31 + 33 + 33 + 36 (powers of 3)

(786 - 330 + 467)3 = 786,330,467

BismillahThe Arabic letters of the opening phrase of the Quran (بسم الله الرحمن الرحيم Bismillah al-Rahman al-Rahim, translated as "In the name of God, Most Gracious, Most Merciful") sum to the numerical value 786 in the system of Abjad numerals.

991 The integer given by formula: 991 · n2 + 1,
is not a perfect square for any natural number n...
Until n = 12005735790331359447442538767. In fact,
991 · 120057357903313594474425387672 + 1 =
= 3795164009068119306380148960802
Postulating general principles based on observations can lead to incorrect conclusions...
BR

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

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