1134

1134 = 2 x 3 x 3 x 3 x 3 x 7.

1134 is the smallest number such that the sum of its proper divisors equals the sum of the sums of proper divisors of its proper divisors.

1134 is the number of permutations of nine items that fix five elements.

1134 is 14014 in base 5.

1134 is divisible by the number of primes below it (189): 1134/189 = 6.

1134 is a concentric 14-gonal (tetradecagonal) number (A195145).

Source: Number Gossip

916

916 = 2 x 2 x 229.

When 916 is raised to the sum of its digits and increased by 1, the result is a prime: 916^{(9 + 1 + 6)} + 1. It is the largest such three-digit number.

916 has a representation as a sum of two squares: 916 = 4² + 30².

916 is a strobogrammatic number (A000787). It appears the same whether it is viewed normally or upside down.

The sum of the digits of 916 (9 + 1 + 6 = 16) is a substring of 916 (A052018).

916 America is an asteroid discovered in 1915 by G.N. Neujmin. There are seven letters in the asteroid's name and seven letters in its discoverer's last name. Note that 916 * 1915 + 7 * 7 is a prime.

Source: Prime Curios!

715

715 = 5 x 11 x 13.

715 is the tenth pentatope number. It is also a pentagonal number (A000326), a hendecagonal number (A051682), and a hexagonal pyramidal number (A002412).

715 is 222111 in base 3, 23023 in base 4, and 1313 in base 8.

715 is the number of intersections of diagonals in the interior of a regular 13-gon (A006561).

715 is the smallest positive number that can be written as a sum of distinct Fibonacci numbers in 26 ways.

Source: Number Gossip

134

134 = 2 x 67.

134² - 67² = 13467.

134 is the maximum number of regions into which 12 circles divide the plane.

134 is 11222 in base 3 and 112 in base 11.

134 is the sum of three distinct positive cubes (A024975): 134 = 5³ + 2³ + 1³. It is also the sum of five positive cubes (A003328): 134 = 4³ + 3³ + 3³ + 2³ + 2³.

Source: Prime Curios!

308

308 = 2 x 2 x 7 x 11.

308 is a heptagonal pyramidal number.

308 is the maximum number of regions into which 18 circles divide the plane.

308³ + 308⁰ + 308⁸ is a prime number.

308 is the sum of two consecutive primes: 308 = 151 + 157.

308 is 102102 in base 3. It is 464 in base 8.

Source: Prime Curios!

704

704 = 2 x 2 x 2 x 2 x 2 x 2 x 11.

704 has a unique representation as a sum of three squares: 704 = 8² + 8² + 24².

704 is the maximum number of regions into which 27 circles divide the plane. It is also a central polygonal number (the maximum number of pieces formed when slicing a pancake with 37 cuts) (A000124).

704 is the number of one-sided octominoes (A000988).

The sum of the fourth power of the prime factors of 704 is a prime (A134620): 6(2⁴) + 11⁴ = 14737.

Source: What's Special About This Number?

496

496 = 2 x 2 x 2 x 2 x 31.

496 is the 31st triangular number. It is the sum of all integers from 1 to 31. It is also a hexagonal number and a centered nonagonal number.

496 is the smallest triangular number such that the sum of its digits cubed is prime: 4³ + 9³ + 6³ = 1009.

496 is the third perfect number, associated with the Mersenne prime 31. It is the largest perfect number with all different digits. It is the smallest perfect number such that the sum of its digits is prime: 4 + 9 + 6 = 19.

496 = 1³ + 3³ + 5³ + 7³.

Source: Number Gossip

2219

2219 = 7 x 317. It is the product of two primes whose sum is a perfect square (A141755): 7 + 317 = 324 = 18².

2219 is the number of 14-hexes with reflectional symmetry (A002215). It is also the number of restricted hexagonal polyominoes with 7 cells (A002212).

2219 is the number of incongruent ways to tile a 5 x 66 room with 1 x 2 Tatami mats, with at most three Tatami mats meeting at a point (A068930).

2219 is a number of the form a^b + c^d, where a, b, c, and d are the first four primes (A168349): 2219 = 2⁵ + 3⁷.

2217 = 3 x 739, 2218 = 2 x 1109, and 2219 are all semiprimes (A115393).

Source: What's Special About This Number?

280

280 = 2 x 2 x 2 x 5 x 7.

280 is 100011000 in base 2 (binary).

280 has a unique representation as a sum of three squares: 280 = 6² + 10² + 12².

The sum of the first 280 consecutive primes mod 280 is prime.

280 is the number of ways 18 people around a round table can shake hands in a non-crossing way, up to rotation.

280 is an octagonal number.

Source: Prime Curios!

578

578 = 2 x 17 x 17.

578 has two representations as a sum of two squares (A118882): 578 = 7² + 23² = 17² + 17².

578 is the number of graphs with 7 vertices with clique number 3.

578 is 210102 in base 3 and 21002 in base 4. It is 242 in base 16 and 123 in base 23.

578 is the smallest of four consecutive integers divisible by four consecutive primes respectively (A072555).

Source: What's Special About This Number?

970

970 = 2 x 5 x 97.

970 has two representations as a sum of two squares: 970 = 3² + 31² = 21² + 23².

970 is a heptagonal number (A000566).

970 is the number of connected graphs with 8 vertices and 17 edges.

970 is 33022 in base 4 and 12340 in base 5.

The sum of the divisors of 970 is a square (A006532): 1 + 2 + 5 + 10 + 97 + 194 + 485 + 970 = 1764 = 42².

Source: What's Special About This Number?

390

390 = 2 x 3 x 5 x 13. The prime factorization of 390 exhibits the smallest digital sum, [(2 + 3 + 5 + (1 + 3)] = 14, of any factorization with four primes with distinct digital sums (2, 3, 5, and 4).

390 is the number of integer partitions of 32 into distinct parts.

390 is the sum of two consecutive primes: 390 = 193 + 197. It is also the sum of four consecutive primes: 390 = 89 + 97 + 101 + 103.

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

390 is 12012 in base 4 and 3030 in base 5. It is 606 in base 8.

Source: Prime Curios!

664

664 = 2 x 2 x 2 x 83.

664 is a value of n such that n(n + 7) is a palindrome (445544).

664 is 554 in base 11 and 474 in base 2.

664 is a generalized heptagonal number (A085787).

664 is the solution to the postage stamp problem for 6 denominations and 7 stamps (A001211).

664 is the sum of three distinct positive cubes (A024975): 664 = 8³ + 5³ + 3³.

Source: What's Special About This Number?

471

471 = 3 x 157.

471 is 111010111 in base 2 (binary) (A006995). It is 333 in base 12 and 727 in base 8.

471 is the smallest number with the property that its first four multiples (471, 942, 1413, 1884) contain the digit 4.

471 is the sum of three consecutive primes (A034961): 471 = 151 + 157 + 163.

471 is the sum of twelve positive fifth powers (A003357): 471 = 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵ + 1⁵ + 1⁵ + 1⁵.

Source: What's Special About This Number?

955

955 = 5 x 191.

955 is the number of ways to arrange the numbers 1 to 9 around a circle so that the sums of adjacent numbers are distinct.

955 is 32323 in base 4 and 353 in base 17.

955 and 955² = 912025 have the same digit sum (A058369): 9 + 5 + 5 = 19 = 9 + 1 + 2 + 0 + 2 + 5. They also have the same initial digit and final digit (A086457).

955 and the 955th prime (7537) have only the digit 5 in common (A107936).

Source: What's Special About This Number?

465

465 = 3 x 5 x 31.

465 is the 30th triangular number (the sum of all integers from 1 to 30).

465 is a Kaprekar constant in base 2.

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

465 is 393 in base 11.

465 is a member of the Padovan sequence.

Source: Zoo of Numbers

943

943 = 23 x 41.

943*349! - 1 is a titanic prime.

943 is a Lucas 6-step number.

943 and the 943rd prime (7451) have only the digit 4 in common (A107935).

943 is the sum of 18 and no fewer nonzero fourth powers (A046049): 943 = 4⁴ + 3⁴ + 3⁴ + 3⁴ + 3⁴ + 3⁴ + 3⁴ + 3⁴ + 3⁴ + 2⁴ + 2⁴ + 1⁴ + 1⁴ + 1⁴ + 1⁴ + 1⁴ + 1⁴ + 1⁴.

Source: Prime Curios!

365

365 = 5 x 73.

365 is 101101101 in base 2 (binary). It is 555 in base 8.

365 is a centered square number and a centered tridecagonal number (A051865).

365 is the smallest number that can be written as a sum of consecutive squares in more than one way: 365 = 14² + 13² = 12² + 11² + 10².

365 has two representations as a sum of two squares: 365 = 2² + 19² = 13² + 14².

365 is the hypotenuse of two primitive Pythagorean triples: 365² = 27² + 364² = 76² + 357².

365 is the most frequent number of days in a year.

Source: What's Special About This Number?

188

188 = 2 x 2 x 47.

188 is the number of connected bipartite graphs with eight vertices.

188 is the largest known even number that can be expressed as the sum of two distinct primes in exactly five ways.

188 is the number of semigroups of order 4.

188³ = 6,644,672 = (6 + 64 + 46 + 72)³.

188 = 2² + 3² + 7² + 11².

188 Menippe is an asteroid discovered in 1878.

Source: Prime Curios!

291

291 = 3 x 97.

291 is the smallest semiprime with prime factors adding up to 100.

291 is the largest number that is not the sum of distinct non-trivial powers.

291 is 2131 in base 5. It is 10203 in base 4 and 1203 in base 6. It is 353 in base 9 (A029955) and 123 in base 16 (A048447).

Inserting a digit '1' between adjacent digits of 291 makes a prime (A050711): 21911 is prime.

291 was an arts and literary magazine published from 1915 to 1916 in New York City.

Source: Number Gossip

1267

1267 = 7 x 181.

1267 is 5511 in base 6. It ends with the digit 7 in bases 9, 10, 12, 14, 15, 18, 20, 21, 28, and 30.

1267 is the sum of two positive fifth powers (A003347): 1267 = 4⁵ + 3⁵.

1267 is the sum of nine consecutive primes (A127336): 1267 = 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 + 163.

1267² = 1605289 contains exactly seven different digits (A054035).

1267 is the maximum number of points visible from some point in a square 45 x 45 lattice (A141224).

Source: On-Line Encyclopedia of Integer Sequences

629

629 = 17 x 37.

629 is a brilliant number (A078972). It is a semiprime whose prime factors have the same number of decimal digits.

629 is a powerful number (A007532). It can be written as a sum of positive powers of its digits: 629 = 6² + 2⁹ + 9².

629 is 2525 in base 6. It is 275 in base 16 and 125 in base 24.

629 has two representations as a sum of two squares: 629 = 2² + 25² = 10² + 23².

629 is the hypotenuse of two primitive Pythagorean triples: 629² = 100² + 621² = 429² + 460².

Source: On-Line Encyclopedia of Integer Sequences

828

828 = 2 x 2 x 3 x 3 x 23.

There are 828 primes between 180,000 and 190,000 (A038824).

There are 828 ways to write 42 as the sum of nine nonnegative cubes (A173682).

828 is the sum of nine positive fifth powers (A003354): 828 = 3⁵ + 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵ + 1⁵ + 1⁵.

828 is a number with 18 divisors (A030636).

The sum of the base 3 digits of 828 (1010200) equals the sum of the base 9 digits of 828 (1120) (A037314).

Source: On-Line Encyclopedia of Integer Sequence

1159

1159 = 19 x 61.

1159 is a centered octahedral number (A001845).

1159 is a member of the Mian-Chowla sequence (A005282).

1159 is the sum of the first 39 nonprimes (A051349).

1159 is the maximum number of points visible from some point in a square 43 x 43 lattice (A141224).

Source: What's Special About This Number?

408

408 = 2 x 2 x 2 x 3 x 17.

408 is the sum of four consecutive primes: 408 = 97 + 101 + 103 + 107. It is also the sum of eight consecutive primes: 408 = 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67.

408 is an octagonal number.

408 is the eighth Pell number.

408 is 3113 in base 5, 1122 in base 7, and 212 in base 14.

408 is the telephone area code for the Silicon Valley, California.

Source: What's Special About This Number?

330

330 = 2 x 3 x 5 x 11.

330 is the eighth pentatope number. It is also a pentagonal number.

330³ + 330³ + 330⁰ is a prime number.

330 is the sum of six consecutive primes: 330 = 43 + 47 + 53 + 59 + 61 + 67.

330 is the sum of five consecutive squares: 330 = 6² + 7² + 8² + 9² + 10².

Source: Prime Curios!

6081

6081 = 3 x 2027.

6081 has a cube that is the sum of three positive cubes.

6081 is 4629 in base 11 and 3629 in base 12.

6081 is a concentric 16-gonal number (A195146). It is also a centered 32-gonal number (A195315).

6081 is the sum of the first 54 primes (A109722).

Source: What's Special About This Number?

615

615 = 3 x 5 x 41. It is the product of three distinct Sophie Germain primes (A157346).

615 is a hypotenuse for which there exist four distinct integer triangles (A084648).

615 is the sum of seven positive fifth powers (A003352): 615 = 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵.

The sum of the even digits of 615 equals the sum of the odd digits of 615 (A036301).

Source: On-Line Encyclopedia of Integer Sequences

527

527 = 17 x 31.

527 is the smallest number n for which there do not exist four smaller numbers so that a₁! a₂! a₃! a₄! n! is square.

527 is 252 in base 15.

527 is a brilliant number (A078972). It is a semiprime whose prime factors have the same number of digits.

Section 527 of the U.S. Tax Code regulates soft money political campaigning.

Source: What's Special About This Number?

603

603 = 3 x 3 x 67.

The first 603 digits of 603⁶⁰³ form a 2002-bit prime.

603 is the smallest number n so that n, n + 1, and n + 2 are all the product of a prime and the square of a prime: 603 = 67 x 3²; 604 = 151 x 2²; 605 = 5 x 11².

603² = 363609 = (3 - 6 - 3 + 609)².

603 is 1133 in base 8, 311 in base 14, and 113 in base 24.

Source: Prime Curios!

1425

1425 = 3 x 5 x 5 x 19.

1425 is 10110010001 in base 2 (binary). It is a self-descriptive number in base 5: 21200.

The sum of the digits of 1425 is equal to the number of divisors of 1425 (1, 3, 5, 15, 19, 25, 57, 75, 95, 285, 475, 1425): 1 + 4 + 2 + 5 = 12 (A057531 and A057532).

1425 is the sum of the first 31 semiprimes (A062198).

Every digit occurs at least once in 1425⁴: 4,123,437,890,625 (A121321).

Source: On-Line Encyclopedia of Integer Sequences

4646

4646 = 2 x 23 x 101.

The digits of 4646 are all semiprimes (A111494 and A107665).

5⁴⁶⁴⁶ - 4646⁵ is a prime (A117705).

4646 and the 4646th prime (44699) contain only the digits 4, 6, and 9 (A107624).

4646 is the number of connected graphs on eight nodes with clique number 4 (A126746).

Source: On-Line Encyclopedia of Integer Sequences

485

485 = 5 x 97.

485 has two representations as a sum to two squares: 485 = 1² + 22² = 14² + 17².

485 is the hypotenuse of two primitive Pythagorean triples: 485² = 44² + 483² = 93² + 476².

485 is the number of categories with six morphisms and two objects.

485 is 345 in base 12. It is 101 in base 22.

Source: What's Special About This Number?

238

238 = 2 x 7 x 17.

238 is the sum of the first 13 primes: 238 = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41.

238 is the number of connected partial orders on six unlabeled elements.

238 is 11101110 in base 2 (binary). It is 3232 in base 4.

238 is a tridecagonal number (A051865).

U-238 is the non-fissile isotope of uranium that is the heaviest isotope of any material available through extraction from minerals.

Source: What's Special About This Number?

660

660 = 2 x 2 x 3 x 5 x 11.

660 is 1010010100 in base 2 (binary). It is 220110 in base 3 and 22110 in base 4.

660 is the order of a non-cyclic simple group.

660 is the sum of four consecutive primes: 660 = 157 + 163 + 167 + 173. It is also the sum of six consecutive primes: 660 = 101 + 103 + 107 + 109 + 113 + 127. And the sum of eight consecutive primes: 660 = 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101.

660 is the number of feet in a furlong.

Source: What's Special About This Number?

3518

3518 = 2 x 1759.

3518 is 24142 in base 6. It is the 40th base-6 palindrome that starts with 2 (A043011).

3518 is the smallest of four consecutive integers divisible by four consecutive primes (A072555): 3518 = 2 x 1759; 3519 = 3 x 3 x 17 x 23; 3520 = 2^6 x 5 x 11; 3521 = 7 x 503.

The constants pi, e, and phi have the same decimal digit in the 3518th place (A090230).

Source: Positive Integers

373

373 is a prime number.

373 is the only palindromic prime with all substrings prime. It is the largest prime such that each substring is prime.

373 is the sum of the squares of five consecutive primes: 373 = 3² + 5² + 7² + 11² + 13².

373 = 2¹ + 3¹ + 5² + 7³ is the sum of the first four primes raised to the powers of the first four Fibonacci numbers.

373 has a representation as a sum of two squares: 373 = 7² + 18².

373 is the hypotenuse of a primitive Pythagorean triple: 373² = 252² + 275².

Water boils at a temperature under standard conditions of about 373 kelvins.

Source: Prime Curios!

741

741 = 3 x 13 x 19.

741 is the 13th triangular number (A000217).

741 is a divisor of 77² - 1.

741 is not expressible as the sum of a prime and a triangular number (A076768).

741 and 742 have three distinct prime factors (A140077).

Source: On-Line Encyclopedia of Integer Sequences

646

646 = 2 x 17 x 19.

646 is a divisor of 69⁶ - 1.

646 is the number of connected planar graphs with 7 vertices (A003094).

646 is 787 in base 9.

646 is the sum of seven positive fifth powers: 646 = 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵.

Source: What's Special About This Number?

3488

3488 = 2 x 2 x 2 x 2 x 2 x 109.

3488 has a fifth root that starts 5.11111. . .

3488 is the number of complete squares that fit inside a circle of radius 34, drawn on squared paper (A119677).

3488 is the number of sums payable using exactly 37 banknotes of denominations 1, 5, 10, 20, 50, 100 (change allowable) (A135526).

3488 has a representation as a sum of two squares: 3488 = 28² + 52².

3488 is a divisor of 33⁴ - 1.

Source: What's Special About This Number?

3480

3480 = 2 x 2 x 2 x 3 x 5 x 29.

3480 is a Perrin number (A001608).

3480 is 110110011000 in base 2 (binary). It is 2020 in base 12.

3480 is an octagonal pyramidal number (A002414).

3480 is the number of ways to place two nonattacking queens on an 10 x 10 board (A036464).

Source: What's Special About This Number?

361

361 = 19 x 19.

361 is a centered triangular number (A005448). It is also a centered octagonal number (A016754) and a centered decagonal number (A062786).

The representations of 361 in bases 2, 3, 4, 5, 6, 8, 9, and 10 all end in 1. It is 551 in base 8 and 441 in base 9. It is 121 in base 18.

361 is a square that remains a square when the last digits is removed (A023110).

361 and 361² (130321) have the same digit sum (A058369): 3 + 6 + 1 = 10 = 1 + 3 + 0 + 3 + 2 + 1.

The game of Go is played on a grid of 19 x 19 lines, which produces 361 intersections on the game board.

Source: On-Line Encyclopedia of Integer Sequences

841

841 = 29 x 29.

841 is a centered square number. It is also a centered heptagonal number and a centered octagonal number.

841 has a representation as a sum of two squares: 841 = 20² + 21². It is the sum of two consecutive squares.

841 is the hypotenuse of a primitive Pythagorean triple: 841² = 41² + 840².

841 is the smallest 3-digit square whose digits are decreasing.

841 is the smallest binary prime square. It's a perfect square whose binary representation (1101001001) considered as a decimal is a prime number.

841 is a divisor of 41⁴ - 1.

Source: Number Gossip

935

935 = 5 x 11 x 17.

935 is a Lucas-Carmichael number (A006972).

The sum of the divisors of 935 is a square (A006532) and a fourth power (A019422): 1 + 5 + 11 + 17 + 55 + 85 + 187 + 935 = 1296 = 36² = 6⁴.

935 is the sum of positive powers of its digits: 935 = 9³ + 3⁴ + 5³ (A007532).

The sum of the digits of 935 is the largest prime factor of 935 (A052021): 9 + 3 + 5 = 17.

Source: What's Special About This Number?

277

277 is a prime number.

76729 is the square of the prime 277 and the smallest square with five or more digits that is the concatenation of three primes (7, 67, and 29).

277 is the smaller prime factor of the semiprime 9000007, the first composite number of the series 97, 907, 9007, and so on.


277 has a representation as a sum of two squares: 277 = 9² + 14².

277 is the hypotenuse of a primitive Pythagorean triple: 277² = 115² + 252².

The digit sum of 277 is a fourth power: 2 + 7 + 7 = 16 = 2⁴.

277 = (2 + 7)² + (7 + 7)².

Source: Prime Curios!

170

170 = 2 x 5 x 17.

170 is 10101010 in base 2 (binary). It is 2222 in base 4.

170 has two representations as a sum of two squares: 170 = 1² + 13² = 7² + 11².

170 is the smallest number that can be written as the sum of the squares of two distinct primes, where each of these primes is the square of a prime added to another prime: 170 = (2² + 3)² + (3² + 2)².

170 is the start of a record-breaking run of consecutive integers (170 to 176) with an odd number of prime factors.

Each internal angle of a regular 36-sided polygon is 170 degrees.

Source: Prime Curios!

926

926 = 2 x 463.

926 is the smallest number that cannot be formed using each of the digits 1 to 6 at most once, with the operators +, -, x, /, and ^.

The digits 926 appear two places after the digits 3.14 in the numbers e^π = 23.14069263. . . and π = 3.141592653. . . .

926 is 222 in base 21.

926 is the sum of six consecutive primes: 926 = 139 + 149 + 151 + 157 + 163 + 167.

Source: What's Special About This Number?

427

427 = 7 x 61.

427 has a unique representation as a sum of three squares: 427 = 9² + 11² + 15².

427 is a value of n for which n! + 1 is a prime (A002981).

427 is 110101011 in base 2 (binary) (A006995) and 1551 in base 6.

427 is the solution to the postage stamp problem for 4 denominations and 10 stamps (A001209).

Source: What's Special About This Number?

919

919 is a prime number.

919 is the 18th centered hexagonal number (hex number).

919 is the smallest palindromic number whose sum of digits (19) shows up as a substring of the number.

919 is the smaller number in the smallest pair of prime numbers that are mutually the sums of the same powers of each other's digits: 919 = 1³ + 4³ + 5³ + 9³ and 1459 = 9³ + 1³ + 9³.

919 is the largest known palindromic prime for which the next prime (929) is also palindromic.

919 is the smallest palindromic prime equal to the difference of consecutive cubes:919 = 18³ - 17³.

Source: Prime Curios!

1287

1287 = 3 x 3 x 11 x 13.

1287 is the binomial coefficient C(13,5) (A000389).

1287 is a divisor of 100³ - 1.

1287 is the smallest value that when multiplied by 7 has only the digits 0 and 9: 1287 x 7 = 9009 (A096688).

A famously long sentence in Absalom, Absalom! by William Faulkner contains 1,287 words.

Source: On-Line Encyclopedia of Integer Sequences