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}  (2^{2} + 3^{2} +
5^{2} + 7^{2})  Trotter & De
Geest
= 43 + 47 + 53 + 59 (sum of 4 consecutive primes)
202 x 11 = 2222 
203 
is
the sixth Bell
number.
203^{2} + 203^{0} + 203^{3} 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)
= 1^{2} + 2^{2} + 3^{2} + 4^{2} +
5^{2} + 6^{2} + 7^{2} + 8^{2} (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)
=
2^{2} x 3 x 17
204^{2} =
23^{3} + 24^{3} + 25^{3}

205 
is
the largest number that cannot be written as the sum of distinct primes of
the form 6n+1.
=
2^{3} + 2^{3} + 4^{3} + 5^{3} (sum
of cubes)

206 
is
the smallest number whose English name contains all five vowels
exactly once (twO hUndrEd And sIx).
=
1^{3} + 2^{3} + 2^{3} + 4^{3} +
5^{3} (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 207^{4} are
a permutation of
the last half of the digits: 1836036801.
= 3^{2} · 23
= 2^{2} + 3^{2} + 5^{2} + 13^{2}
CIVIC is
a palindrome and the anagram of the Roman numeral CCVII (207).

208 
is
a tetranacci
number.
is
a divisor of 25^{2}  1
=
2^{4} x 13
= 8^{2} + 12^{2}
= 2^{8}  48
= 2^{2} + 3^{2} + 5^{2} + 7^{2} +
11^{2}  Sladcik
= 2^{3} + 2^{3} + 4^{3} + 4^{3} +
4^{3}

209 
is
a Harshad
number and the smallest quasiCarmichael
number in base 9.
is the smallest number with 6 representations as a sum of 3 squares:
209 = 1^{2} + 8^{2} + 12^{2} = 2^{2} +
3^{2} + 14^{2} = 2^{2} + 6^{2} +
13^{2} = 3^{2} + 10^{2} + 10^{2} =
4^{2} + 7^{2} + 12^{2} = 8^{2} +
8^{2} + 9^{2}
The
curve 42x^{2}  y^{2} = 209
contains the 'prime points' (3, 13), (5, 29), (7, 43), and (13,
83)  Buddenhagen
88
+ 209 = 297 and 88,209 = 297^{2 }(see
number 494 furtherbelow)
=
1^{6} + 2^{5} + 3^{4} + 4^{3} +
5^{2} + 6^{1}  posted by Jim
O'Donohoe
= 3^{3} + 3^{3} + 3^{3} + 4^{3} +
4^{3}
= 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.
=
3^{5}  2^{5}
= 67 + 71 + 73 (sum of consecutive primes)

212 
is
the lowest even 3digit integer, ABC, such that (ABC)/(A
x B x B) is also prime.
curiously, 4 out of 5 digits of 212^{2} are the same (44944).
212° Fahrenheit = 100° Celsius (the boiling point of water)
= 2^{2} x
53 
213 
=
3 x 71
= 2^{3} + 2^{3} + 2^{3} + 4^{3} +
5^{3} 
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
= 2^{3} + 3^{3} + 3^{3} + 3^{3} +
5^{3} 
215 
=
6^{3} + ( 1)^{3} = 6^{3} 
1^{3} (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: 3^{3} + 4^{3} +
5^{3}
= 216 = 6^{1+2
}= 216 = [(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:

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)
= 1^{3} + 6^{3} = ( 8)^{3} + 9^{3} (sum
of cubes)
= 9^{3}  8^{3} (difference
of consecutive cubes)

218 
is
a nontotient
number, and the number of 4vertex digraphs.
=
7^{2} + 13^{2} (sum of squares)  Walter
Seaman
= 7^{3}  5^{3} (difference of cubes)

219 
is
a semiprime
number, and the number of space
groups, not including mirror images.
=
3^{3} + 4^{3} + 4^{3} + 4^{3}

220 
is
the smallest amicable
number.
= 47
+ 53 + 59 + 61 (sum of consecutive primes) 
221 
is
the number of 7vertex Hamiltonian planar
graphs.
221b,
Baker Street, London, England is the address of Sherlock Holmes.
=
10^{2} + 11^{2}
= 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 10^{n }+ 7)/9
=
71 + 73 + 79 (sum of consecutive primes)
= 19 + 23 + 29 + 31 + 37 + 41 + 43

224 
=
2^{5} x 7
= 2^{3} + 3^{3} + 4^{3} + 5^{3} (sum
of consecutive cubes)
= 2^{8}  2^{5} 
225 
is
an octagonal
square number.
=
113^{2}  112^{2}
= (1 + 2 + 3 + 4 + 5)^{2}
= 1^{3} + 2^{3} + 3^{3} + 4^{3} +
5^{3
}= 3^{2} x 5^{2} = 15 x 15

226 
is
a centered
pentagonal number.
=
2 x 113
= 2(7^{2} + 8^{2})

227 
is
a prime number and twin
prime with 229, it is also the number of 8edge 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]
= 2^{3} + 3^{3} + 4^{3} + 4^{3} +
4^{3
}227^{n} = 233^{n} + 239^{n} 
251^{n}  257^{n} + 263^{n} ,
with n = 1, 2
2^{227} 
1 is the smallest composite Mersenne
number about which we don't know the divisors.

228 
is 77gonal
number and an abundant
number.
=
444 in base 7.
= 2^{2} 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)
=
4^{4}  3^{3}

230 
is
the number of space
groups, describing all possible crystal symmetries.
=
6^{2} + 7^{2} + 8^{2} + 9^{2 }(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.
=
2^{2} + 3^{2} + 7^{2} + 13^{2 }(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.
=
2^{3} x 29
= 2^{4} + 6^{3} = 2^{3}(2^{2} +
5^{2}) = 2(4^{2} + 10^{2})

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 3digit 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 3^{2} x 13
= 3^{5}  3^{2}
= 3^{2} + 15^{2
}=
2(6^{2} + 9^{2})

235 
is
a centered
triangular number (= [3xn^{2} + 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 )

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
=
2^{2} x 59
= 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 (sum
of first consecutive primes)

237 
is
the smallest 3digit 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 = 5^{3} + 3 x 3^{3} + 4 x 2^{3} + 1^{3 }(=
9 cubes)
239
= 2 x 4^{3} +
4 x 3^{3} +
3 x 1^{3 }(=
9 cubes) ...
etc.
239^{2} =
2 x 13^{4 } 1
This
prime number appears in one of the earliest known geometrically
converging formulas for computing :
/4
= 4 arctan(1/5)  arctan(1/239)

240 
is
the smallest number with 20 divisors.
n^{x } n^{x4} 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)
= (2^{8} + 4^{8} + 1^{8}) / (2^{4} +
4^{4} + 1^{4})
can
be represented as:
241 = 4^{2 }+ 15^{2} = 3^{2 }+ 6^{2} +
14^{2} = 6^{2} + 6^{2} + 13^{2
}is
the sum of 170 and its reverse:
241 = 170 + 071
241^{2 }=
29281^{2 }+ 50160^{2}
241^{2} = 29041^{2 } 29040^{2 }(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
= 3^{5}
= 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.
=
1^{3} + 3^{3} + 6^{3} (sum
of cubes)

245 
is
a stella
octangula number.
= 5 x 7^{2}
= 8^{2} + 9^{2} + 10^{2} (sum
of consecutive squares) 
246 
= _{9}C_{2} + _{9}C_{4} + _{9}C_{6}
=
2 x 3 x 41
= 3^{3} + 3^{3} + 4^{3} + 4^{3} +
4^{3} (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 
=
2^{8}  2^{3}

249 
=
3 x 83 
250 
=
2 x 5^{3} 
251 
is
the smallest number that can be written as the sum of 3 cubes in
2 ways:
= 2^{3} + 3^{3} + 6^{3} = 1^{3} +
5^{3} + 5^{3} 
252 
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.

253 
is
the lowest nontrivial triangular
star number.
=
1 + 2 + 3 + … + 20 + 21 + 22
= 1⁄2 (22 x 23)
= 4^{3} + 4^{3} + 5^{3}

254 
=
2^{8}  2^{1} 
255 
=
11111111 in base 2.
255
x 807 = 205785
(the product has the same digits as its factors)

256 
is
the smallest 8^{th} power (besides 1):
= 2^{8} = 4^{4} = 16^{2}
=
1 0000 0000_{2}
= 100_{16}
=
2^{9}  2^{8}
= 4^{3} + 4^{3} + 4^{3} + 4^{3
}=
3^{5} + 3^{2} + 3^{1} + 3^{0}
256
= 2 x 5 +
6

257 
is
a Fermat
prime.
_{=
2}2^{3}_{+
1}
=
1^{8} + 2^{8}
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
= 6^{1} + 6^{2} + 6^{3}
= 59 + 61 + 67 + 71 (sum of consecutive primes) 
259 
=
1111 in base 6.
= 1^{3} + 2^{3} + 5^{3} + 5^{3}
= 2^{3} + 2^{3} + 3^{3} + 6^{3} 
260 
is
the constant of a 8x8 magic square.
= 2^{2} 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 16gon into
7 quadrilaterals. 
262 
is
the 9^{th} 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 n^{2} + 1 is
a prime:
264^{2} + 1 = 69697
seems to be the largest number whose square is 'undulating': 264^{2} = 69696
n^{10} 
1 is divisible by 264 if n is prime and n > 3.
= 2^{5} + 6^{3} + 4^{2
}= 2^{3} + 4^{3} + 4^{3} + 4^{3 }+
4^{3} (sum of five cubes)^{
}= 17^{2}  5^{2} (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:
265^{2} = 23^{2} + 264^{2} = 96^{2} +
247^{2}
is the number of derangements of
6 items.
=
11^{2} + 12^{2} (sum of consecutive
squares)
= 3^{2} + 16^{2}
=
!6 = 6!(1  1/1! + 1/2!  1/3! + 1/4!  1/5! + 1/6!)

266 
is
a divisor of 11^{3}  1.
=
2^{3} + 2^{3} + 5^{3} + 5^{3 }(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.
=
1^{3} + 2^{3} + 2^{3} + 5^{3} +
5^{3}
= 2^{3} + 2^{3} + 2^{3} + 3^{3} +
6^{3} (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 nonleap year is 26 September (26/9).
 Claudio Meller

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.
270^{2} + 1 is prime.
10! has 270 divisors.
=
19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 (sum of
consecutive primes)
= 3^{3} + 3^{3} + 6^{3 } (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).
Owls
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.
=
10^{3}  9^{3} (difference of
cubes)
=
7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 (sum
of consecutive primes)

272 
is
the 7^{th} Euler
number.
= 16 x 17 = 17^{2 } 17^{1}
= 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 thirtythree seconds.
In other words, the entire piece consists of silences!

274 
is
a tribonacci
number: 44 + 81 + 149
sum of cubes: 2^{3} + 2^{3} + 2^{3} + 5^{3} +
5^{3} 
275 
=
5^{2} x 11 
276 
is
the sum of the first three 5^{th} powers:
= 1^{5} + 2^{5} + 3^{5} 
277 
is
a prime and
a Perrin
number.
=
(2 + 7)^{2} + (7 + 7)^{2}
= 3^{3} + 5^{3} + 5^{3} (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.
= 2^{3} 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 multidigit palindrome sandwiched between twin
primes: 281 and 283. 
283 
is
a prime number.
= 2^{5} + 8 + 3^{5} 
284 
is
an amicable
number (with 220).
= 2^{2} x 71 
285 
=
1^{2} + 2^{2} + 3^{2} + … + 7^{2} +
8^{2} + 9^{2} (sum of consecutive
squares) 
286 
is
a tetrahedral
number.
is the number of rooted
trees with 9 vertices.
=
C_{13}^{3} = C_{13}^{10}

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 nonpalindrome and
nonsquare that when multiplied by its reverse gives a square:
288 x 882 = 504^{2}
= 4!
x 3! x 2! x 1! 
289 
is
a square (17^{2})
with nondecreasing digits.
=
1^{3} + 2^{3} + 4^{3} + 6^{3}
= 0^{0} + 1^{1} + 2^{2} + 3^{3} +
4^{4}
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)
= 2^{3} + 2^{3} + 3^{3} + 5^{3} +
5^{3} (sum of cubes)

294 
=
2 x 3 x 7^{2}
11115^{2}  294^{2} =
123,456,789 
295 
=
5 x 59 
296 
=
2^{3 }x 37 
297 
is
a Kaprekar
number:
297^{2} = 88 209; 297 = 88 + 209 
298 
=
2 x 149 
299 
is
the smallest number whose sum of digits is 20.
is a selfnumber.
=
13 x 23
is
the maximum number of pieces into which a 3dimensional 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.
=
2^{2} x 3 x 5^{2}
=
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 XV^{xx}, or III^{c}.
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.
"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 6hyperperfect
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 
=
9^{2} + 10^{2} + 11^{2} (sum
of consecutive squares) 
303 
is
a lucky
number.
its
cubic power is a concatenation of other cubes:
303^{3} = 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 = 2^{4} x 19 and
27 = 2 x 4 + 19
=
41 + 43 + 47 + 53 + 59 + 61 (sum of consecutive
primes)

305 
is
the 5^{th} 'hexagonal prism' number. An hexagonal prism
number is of the form (n + 1)(3n^{2} +
3n + 1).
305^{2} =
207^{2} + 224^{2} = 136^{2} + 273^{2 }(Pythagorean
triple)
=
5 x 61

306 
=
2 x 3^{2} x 17
= 71 + 73 + 79 + 83 (sum of consecutive primes) 
307 
is
a prime,
and a nonpalindrome having a palindromic square:
307^{2} = 94249
= 1^{3} +
5^{3} + 3^{3} (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 hateoriented.

312 
=
2^{3} x 3 x 13
= 2222 in base 5.
312^{2} =
14^{3} + 15^{3} + 16^{3 }+ 17^{3} +
18^{3 }+ 19^{3} + 20^{3} + 21^{3 }+
22^{3} + 23^{3} + 24^{3} + 25^{3}

313 
is
a palindromic
prime.
is the only 3digit 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]
=
12^{2} + 13^{2}
3443
/ 313 =11
37873 / 313 = 121
(all terms are palindromic!)
313^{2} =
25^{2} + 312^{2} (Pytagorean triple)
10^{313} +
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 
=
3^{2} x 5 x 7
= (4 + 3)(4 + 1)(4 + 5)
= (10  3)(10  1)(10  5)
= 7! / 4^{2}
= 8! / 2^{7} 
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
3^{4} + 4 x 2^{4} + 12 x 1^{4}
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.
=
2^{6 }· 5 = 2^{5} · (2·5)

322 
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. 
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 
=
18^{2}
= 73 + 79 + 83 + 89 (sum of consecutive primes)
324 = 3^{2} x 4
324!
 1 is prime...

325 
is
a 3hyperperfect
number.
= 1^{2} + 18^{2}
= 6^{2} + 17^{2}
= 10^{2} + 15^{2
}= 5^{2} 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)
= 6^{2} + 7^{2} + 8^{2} + 9^{2} +
10^{2} (sum of consecutive squares)
= _{11}C_{4} 
331 
is
a prime number.
= 11^{2}  10^{2
}=
59 + 61 + 67 + 71 + 73 (sum of consecutive primes)

333 
is
the number of 7hexes.
is a halfevil
number: 666/2
represents the millesimal finenes of 8 carat.
= 3^{2} x 37
= 370  37
Number
patterns:
166,500,333 =
166^{3 }+ 500^{3} + 333^{3}
333,667,000
= 333^{3 }+ 667^{3 }+
000^{3}
333,667,001
= 333^{3} + 667^{3 }+
001^{3}

335 
is
divisible by the number of primes below it. 
336 
336
x 951 = 319530
(the product has the same digits as its factors)
=
2^{4} x 3 x 7
= _{8}P_{3}
=
6 x 7 x 8

337 
is
a permutable prime with
373 and 733.
is a 4dimensional
centered cube prime (primes of the form n^{4}+(n+1)^{4} )
_{= 2}2^{3} _{+} _{3}2^{2} _{
Kulsha}

338 
=
2 x 13^{2} 
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 5658 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)
=
4^{1} + 4^{2} + 4^{3} + 4^{4 }(sum
of powers of 4)
= 12^{2} + 14^{2} = 4^{2} + 18^{2}

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^{(3411)} is 1 modulo 341.
is a star number.
=
11 x 31
= 37 + 41 + 43 + 47 + 53 + 59 + 61 (sum of consecutive
primes)
= 4^{0} + 4^{1} + 4^{2} + 4^{3} +
4^{4} (sum of powers of 4)

342 
=
= 2 x 3^{2} x 19
= 666 in base 7.
= 18 x 19
= 1^{3} + 5^{3} + 6^{3} = 7^{3} 
1^{3} 
343 
= 343 =
(3 + 4)^{3 }(autothecal
number)
= 18^{0} + 18^{1} + 18^{2} 
344 
is
an octahedral
number: 8(2 x 8^{2} + 1)/3
= 2^{3} x 43
= 4^{3} + 4^{3} + 6^{3} = 1^{3} +
7^{3} 
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
+ 7^{3} 
348 
=
2^{2} 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 5^{2 }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.
= 3^{3} x
13
= 61 + 67 + 71 + 73 + 79 (sum of consecutive primes) 
352 
are
the different arrangements of 9 nonattacking Queens on an 9
by 9 chessboard.
=
2^{2} x 11
= 173 + 179 (sum of consecutive primes)

353 
is
the smallest number whose 4^{th} power can be written
as the sum of four 4^{th} powers:
353^{4 }= 30^{4} + 120^{4} + 272^{4} +
315^{4}
= 13
+ 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 (sum
of consecutive primes) 
354 
=
1^{4} + 2^{4} + 3^{4} + 4^{4} (sum
of the first four 4^{th} powers)
= 354 = 3(5!
 4)^{ }(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 60^{2}/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.
=
2^{3} x 3^{2} 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 (9^{2} + 10^{2}) 
363 
=
3 x 11^{2}
= 3^{1} + 3^{2 }+ 3^{3 }+ 3^{4 }+
3^{5}
= 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59
(sum of consecutive primes)
363^{2} +
484^{2} = (11 x 55)^{2} (quasipalindromic 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)
= _{14}C_{3 }= _{14}C_{11 }(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:
= 10^{2} + 11^{2} + 12^{2} = 13^{2} +
14^{2} 
366 
is
the number of days in a leap year.
= 8^{2} + 9^{2 }+ 10^{2}+ 11^{2} 
367 
is
known as the largest number whose square has strictly increasing
digits: 367^{2} = 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:
3^{3} + 7^{3} + 0^{3}
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:
3^{3} + 7^{3} + 1^{3}
=
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.
=
2^{2} x 3 x 31
=
31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 (sum of
consecutive primes)

373 
is
a permutable prime.
=
3^{2} + 5^{2} + 7^{2} + 11^{2} +
13^{2} (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 5^{3}

376 
is
an automorphic
number:
376^{2} = 141376
376^{3} = 53157376
376^{4} = 19987173376 ...
=
2^{3} x 47

377 
is
the 14^{th} 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 7vertex Hamiltonian
graphs.
=
101 + 131 + 151 (sum of 3 consecutive palindromic
numbers)

384 
=
2^{7} x 3
= 3 x 8 x 4^{2}
= 53
+ 59 + 61 + 67 + 71 + 73 (sum of consecutive primes) 
385 
=
5 x 7 x 11
is a square
pyramidal number because:
1^{2} + 2^{2} + 3^{2} + … + 8^{2} +
9^{2} + 10^{2 }= 385
is the number of partitions of
18.
=
193^{2}  192^{2}

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.
=
2^{3 }x 7^{2}

399 
is
a value of n for which n!+1 is prime.
is a Harshad
number and the smallest LucasCarmichael
number.
=
7^{1} + 7^{2} + 7^{3}
= 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 = 31^{2}
= 1111 in base 7.
= 7^{0} + 7^{1} + 7^{2} + 7^{3}
= 7^{0} + 7^{1} + 7^{2} + 18^{0} +
18^{1} + 18^{2}
= 12^{2} + 16^{2 }(sum
of 2 squares)
= 52^{2}  48^{2 }(difference
of 2 squares)
= 2^{4} x 5^{2}
= 1 + 3 + 5 + … + 35 + 37 + 39 (sum of consecutive
odd numbers)
400
is the number of years in the repeating cycle of leap/nonleap
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.
= 7^{2} + 8^{2} + 12^{2} + 12^{2} 
402 
=
3^{3} + 5^{3} + 5^{3} + 5^{3}
= 2 x 3 x 67 
403 
=
2^{3} + 3^{3} + 3^{3} + 5^{3} +
6^{3}
= 13 x 31 
405 
is
a pentagonal
pyramidal number.
= 4^{3} + 5^{3} + 6^{3}
= 3^{4} + 3^{4} + 3^{4} + 3^{4} +
3^{4} 
406 
=
1^{3} + 4^{3} + 5^{3} + 6^{3
}= 1^{3} + 2^{3} + 3^{3} + 3^{3} +
7^{3}
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:
4^{3} + 0^{3} + 7^{3}
=
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
=
7^{2} + 19^{2} = 11^{2} + 17^{2}
=
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 
=
7^{2} + 8^{2} + 9^{2} + 10^{2} +
11^{2} (sum of consecutive squares)
= (4^{5} + 1^{5} + 5^{5}) / (4 + 1 + 5) 
416 
416,768 = 768^{2} – 416^{2}
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 13^{11}  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 conartist or confidence
trickster.

421 
is
a twin
prime number and a centered
square number.
is the name of a French dice game ('Quatrecentvingtetun').
= 111 in base 20
= 14^{2} + 15^{2} (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 
=
5^{2} x 17
= 8^{2} + 19^{2}
= 13^{2} + 16^{2}
= 5^{2} + 20^{2
}= 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:
428^{2} = 183 184
= 2^{2} x
107

429 
is
a sphenic
number, and the 7^{th} Catalan
number.
is
a divisor of 100^{3}  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:
3^{4} + 11^{4} + 13^{4} = 43283

430 
is
a sphenic
number.
=
2 x 5 x 43

431 
is
a Chen
prime.
431/510
= log_{10}7 (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 3^{3} x 2^{2
}= 103 + 107 + 109 + 113 (sum of consecutive
primes)
= 12^{3} 
6^{4}  G. Sarcone
=
12^{2} + 12^{2} +
12^{2}
= 6^{3} + 6^{3} 
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 10^{2 }is an average person’s heartbeats in a
day.
Four
hundred thirtytwo 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 10^{3}). 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.
=
(13^{3}  11^{3}) / 2

434 
=
3^{3} + 4^{3} + 7^{3} (sum
of cubes)
= 11^{2} + 12^{2} + 13^{2} (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.
=
2^{2} 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
=
2^{2} x 5 x 11
= 21^{2}  1^{2}
= 27^{2}  17^{2}
= 57^{2}  53^{2}
= 111^{2}  109^{2} (differences
of squares)
= 2^{3} + 3^{3} + 4^{3} + 5^{3} +
6^{3} (sum of consecutive cubes)

441 
is
the smallest square which
is the sum of 6 consecutive cubes:
1^{3} + 2^{3} + 3^{3} + 4^{3} +
5^{3} + 6^{3}
=
3^{2} x 7^{2} = 21^{2}
= 29^{2}  20^{2}
= 35^{2}  28^{2}
= 75^{2}  72^{2}
= 221^{2}  220^{2} (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 3digit nonpalindromic prime whose binary equivalent
is a palindromic prime: 110111011 
444 
is
the largest known n for which there is a unique integer solution
to a_{1}+...+a_{n}= (a_{1})...(a_{n}).
= 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.
=
9^{2} + 10^{2} + 11^{2} + 12^{2}

448 
is
the number of 10iamonds.
= 2^{6} x 7 
450 
is
the sum of two consecutive primes:
223 + 227
=
(5 + 4)(5 + 5)(5 + 0)
= 3^{2} + 21^{2}

454 
is
the largest number known that cannot be written as a sum of 7 or
fewer cubes. 
455 
= _{15}C_{3}
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 
=
3^{3} 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
= _{11}C_{5} 
463 
is
a prime number.
is the sum of seven consecutive primes:
53 + 59 + 61 + 67 + 71 + 73 + 79 
464 
=
2^{4} x 29
464^{2} +
777^{2} = (5 x 181)^{2} (quasipalindromic 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.
= 2^{2} x 3^{2} 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.
n^{8 }– 1 is divisible by 480 if n is
prime and n > 5
n^{9}– 1 is divisible by 480 if n is
odd and n > 1 
481 
=
15^{2} + 16^{2} (sum of 2 consecutive integers) 
483 
is
the last 3digit string in the decimal expansion of . 
484 
is
a palindromic square number.
= 22^{2}
= 2^{2} x 11^{2} 
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 7^{2} 
494 
494 +
209 = 703 and 494,209 = 703^{2
}moreover 297+703 = 1000
= 2 x
13 x 19 
495 
is
the Kaprekar
constant for 3digit 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
=
3^{2} x 5 x 11

496 
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:
(2^{n}  1) x 2^{n1}.
=
16 x 31
= 1^{3} + 3^{3} + 5^{3} + 7^{3}

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
499^{3} =
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 wellknown car appreciated worldwide by car
enthusiasts.
= 2^{2} x 5^{3}
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".
=
17^{2} + 18^{2 }(sum of 2 consecutive
squares)
613^{2} =
35^{2} + 612^{2} (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).
=
2^{3} x 7 x 11
= (9^{2} + 10^{2} + 11^{2} + 12^{2} +
13^{2}) + 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 reexamining
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).

625 
is
a centered
octagonal number.
is the hypotenuse of a Pythagorean triple:
625^{2} = 336^{2} + 527^{2}
is an automorphic
number:
625^{2} = 390625
625^{3} = 244140625
625^{4} = 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:
5^{4} = 2^{4} + 2^{4} +
3^{4} + 4^{4} + 4^{4}
=
73 + 79 + 83 + 89 + 97 + 101 + 103 (sum of consecutive
primes)
=
5^{4}
= 25^{2}
= 7^{2} + 24^{2} (solution of a^{2} + b^{2} = z^{4})
= 15^{2} + 20^{2 } (solution of a^{2} + b^{2} = z^{4})
625^{2} +
1 250^{2} =
125^{3}
625^{3} +
1 250^{3} =
46,875^{2}
2
fourth powers share the same digits:
5^{4} = 625 and
4^{4} = 256

648 
64
x 8
64 / 8
64 + 8
64  8 
=
=
=
= 
512
+
8 +
72 +
56 = 

648
 
648
= 16^{2}  17^{2} + 18^{2} + ... + 30^{2} 
31^{2} + 32^{2} =
= 33^{2} + 34^{2}  35^{2} + ... + 46^{2} 
47^{2} + 48^{2}
648
= 83^{2}  79^{2}, 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 53^{6} – 1; also: 2 x 648  1 and 2 x
648 + 1 divide 2^{648}  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 = 2^{3 }x 3^{4}).
• 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 2^{2} divide
648; also: 3 and 3^{2} divide 648.
Moreover:
648^{1/6} = 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
= 1^{2} x 2^{3} x
3^{4}
648
= 18^{2} + 18^{2} = 6^{3} + 6^{3} +
6^{3}

666 
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:
15^{2} + 21^{2}
is the sum of the squares of the first 7 primes:
2^{2} + 3^{2} + 5^{2} + 7^{2} +
11^{2} + 13^{2} + 17^{2}
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 666^{6}. (There
are also exactly six 6's in the previous sentence!)
=
18691113009329  18691113008663 (difference of
2 consecutive prime numbers)
= 1^{6}  2^{6} + 3^{6}
= 6 + 6 + 6 + 6^{3} + 6^{3} + 6^{3}
= 1^{3} +
2^{3} + 3^{3} + 4^{3} + 5^{3} +
6^{3} + 5^{3} + 4^{3} + 3^{3} +
2^{3} + 1^{3}
= 3(6^{3} +
6)
= 2
x 3^{2} 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)
=
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 (10^{666})! is called "Leviathan
number", because this incalculable number has approximately
6.656x10^{668} decimal digits. The number of trailing
zeroes in the Leviathan number is 25x10^{664}143. 
C. Pickover
Tuesday, 6
June 2006 is 060606; 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 newlyweds.
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 computerscanner 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 666 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'.
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 .

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
= _{13}C_{4}

729 
is
a centered
octagonal number (of the form 4n^{2} 
4n + 1).
is the smallest odd cube represented as the sum of 2 primes: 729
= 2 + 727
=
3^{6} = 9^{3} = 27^{2} (perfect
6th power)
= 45^{2}  36^{2} (difference
of squares)
= 1^{3} + 6^{3} + 8^{3} (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.
=
3^{1} + 3^{3} + 3^{3} + 3^{6 }(powers
of 3)
(786  330 +
467)^{3} = 786,330,467
The
Arabic letters of the opening phrase of the Quran (بسم الله الرحمن الرحيم Bismillah
alRahman alRahim, 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 · n^{2} +
1,
is not a perfect square for any natural number n...
Until n = 12005735790331359447442538767.
In fact,
991 · 12005735790331359447442538767^{2} + 1 =
= 379516400906811930638014896080^{2}
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?"
