338

338 = 2 x 13 x 13.

338 is the last integer for which the number of divisors (6) and the sum of its prime factors (2 + 13 + 13 = 28) are both perfect numbers.

338 is 2323 in base 5 and 242 in base 12.

338 has two representations as a sum of two squares: 338 = 7² + 17² = 13² + 13².

338 is a divisor of 99⁴ - 1.

338³ = 38,614,472 = (386 + 1 - 4 - 47 + 2)³.

Source: Prime Curios!

620

620 = 2 x 2 x 5 x 31.

620 is the number of one-sided 7-hexes (or hexagonal polyominoes with 7 cells) (A006535).

620 is the sum of four consecutive primes (A034963): 620 = 149 + 151 + 157 + 163. It is also the sum of eight consecutive primes (A127335): 620 = 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97.

The sum of the first 620 primes is a prime number (A013916).

620 is the sum of twelve positive fifth powers (A003357): 620 = 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵ + 1⁵ + 1⁵ + 1⁵ + 1⁵ + 1⁵.

Source: What's Special About This Number?

216

216 = 2 x 2 x 2 x 3 x 3 x 3.

216 = 6³ is a perfect cube. 216 = 6^{(2 + 1)}.

216 = 21 + 20 + 19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6.

216 is the smallest cube that can be written as the sum of three cubes: 216 = 5³ + 4³ + 3³.

216 is the smallest number that can be expressed as the difference of the sums of the squares of successive twin primes: 216 = (13² + 11²) - (7² + 5²).

216 is 1331 in base 5.

216 is the sum of a twin prime pair: 216 = 107 + 109.

In the film Pi, Max Cohen becomes obsessed with a 216-digit number in his quest to find a numeric equation behind existence.

Source: Prime Curios! and Wikipedia

539

539 = 7 x 7 x 11.

539 is the number of multigraphs with five vertices and nine edges.

539 is 2255 in base 6 and 1400 in base 7.

539 is the sum of two distinct positive cubes (A024670): 539 = 8³ + 3³.

Inserting the digit 9 between adjacent digits of 539 makes a prime (A050719): 59399.

539 is the sum of 11 consecutive primes (A127338): 539 = 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71.

Source: What's Special About This Number?

406

406 = 2 x 7 x 29.

406 is the 28th triangular number. It is the sum of the first 28 positive integers.

406 is a centered nonagonal number.

406 is the number of ways to tile a 3 x 17 rectangle with 3 x 1 rectangles.

406 = 1³ + 4³ + 5³ + 6³ = 1³ + 2³ + 3³ + 3³ + 7³.

406 is 626 in base 8 and 210 in base 14.

406 is the title of a poem by John Boyle O'Reilly.

Source: What's Special About This Number?

120

120 = 2 x 2 x 2 x 3 x 5.

120 has a unique representation as a sum of three squares: 120 = 2² + 4² + 10².

120 = 5!

120 is the 15th triangular number. It is the sum of the first 15 positive integers.

120 is the eighth tetrahedral number.

120 is a hexagonal number.

120 = 3¹ + 3² + 3³ + 3⁴.

120 is the smallest composite number of the form x! whose digit sum (1 + 2 + 0 = 3) and x (5) are both primes.

120 is the smallest three-digit number that may be expressed as the difference between squares of consecutive primes in tow different ways: 120 = 31² - 29² = 17² - 13².

The great rhombicosidodecahedron is an Archimedean solid with 120 vertices, 180 edges, and 62 faces.

Source: Prime Curios!

788

788 = 2 x 2 x 197.

788 has a representation as a sum of two squares: 788 = 2² + 28².

788 is the smallest of six consecutive numbers divisible by six consecutive primes: 788 is divisible by 2, 789 by 3, 790 by 5, 791 by 7, 792 by 11, 793 by 13.

788 is 404 in base 14.

788² is the sum of two successive primes (A074924): 788² = 620944 = 310463 + 310481.

Source: Prime Curios!

236

236 = 2 x 2 x 59.

The product of the digits (2 x 3 x 6 = 36) of 236 is the reverse of the sum of its prime factors (2 + 2 + 59 = 63).

236 is the number of possible moves in Othello (Reversi) after two moves by both players.

236 is the sum of 12 consecutive primes: 236 = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41.

236 is 282 in base 9.

Source: Prime Curios!

155

155 = 5 x 31.

155 has the representation 155 = 2⁷ + 27.

155 = 2² + 3! + 5! + 7² -11 - 13.

155 is the only three-digit number such that 155¹⁵⁵ - 155 + 1 is prime.

155 is the sum of its prime factors plus the primes between these two prime factors: 155 = 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31.

155 = 3³ + 4³ + 4³.

155 = 5¹ + 5² + 5³.

Source: Prime Curios!

872

872 = 2 x 2 x 2 x 109.

872 has a representation as a sum of two squares: 872 = 14² + 26².

872 is the maximum number of regions into which 30 circles can divide the plane.

872! + 1 is a factorial prime.

872 is 464 in base 14.

Source: Prime Curios!

682

682 = 2 x 11 x 31.

682 is 1010101010 in base 2 (binary). It is 22222 in base 4 (A014192) and 262 in base 17.

682 x 682! + 1 is a prime number.

682 is the sum of four consecutive primes (A034963): 682 = 163 + 167 + 173 + 179. It is also the sum of 10 consecutive primes (A127337): 682 = 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89.

682 is the sum of 12 positive fifth powers (A003357): 682 = 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵ + 1⁵ + 1⁵ + 1⁵.

Source: Prime Curios

584

584 = 2 x 2 x 2 x 73.

584 is the number of ways to color the vertices of a triangle with 12 colors, up to rotation.

584 has a representation as a sum of two squares: 584 = 10² + 22².

584 is 248 in base 16.

584 is the sum of three distinct positive cubes (A024975): 584 = 8³ + 4³ + 2³.

Source: What's Special About This Number?

1612

1612 = 2 x 2 x 13 x 31.

1612 has a unique representation as a sum of three squares: 1612 = 6² + 26² + 30².

1612 is a divisor of 25⁶ - 1.

1612 is 22422 in base 5 and 11244 in base 6. It is 727 in base 15.

1612 is the number of primes between 2¹⁴ and 2¹⁵ (A036378).

1612 is the sum of the first 33 semiprimes (A062198).

Source: On-Line Encyclopedia of Integer Sequences

1521

1521 = 3 x 3 x 13 x 13.

1521 is a perfect square: 1521 = 39².

1521 is the smallest number that can be written as the sum of four distinct cubes in three ways: 1521 = 11³ + 5³ + 4³ + 1³ = 10³ + 8³ + 2³ + 1³ = 9³ + 8³ + 6³ + 4³.

1521 has a representation as a sum of two squares: 1521 = 15² + 36².

1521 is a divisor of 22³ - 1.

1521 is a centered octagonal number.

Source: What's Special About This Number?

1413

1413 = 3 x 3 x 157.

1413 is the smallest number that cannot be formed using the digits 0 to 7 at most once, together with the arithmetic operations (symbols) +. -. *, and / (A060315).

1413 has a representation as a sum of two squares: 1413 = 18² + 33².

1413 is 999 in base 12 (A048336). It is 585 in base 16.

1413 has the representation 1413 = 2 x 3⁶ - 45.

Source: What's Special About This Number?

295

295 = 5 x 59.

2 x 295 + 9 x 295 + 5 * 295 + 1 is a prime number (4271).

295 is a structured deltoidal hexecontahedral number.

295 is a centered tetrahedral number (A005894).

295 is 171 in base 14.

295 is the number of primes less than 44² = 1936 (A038107).

The sum of the digits of 295 is a square (A028839): 2 + 9 + 5 = 16 = 4².

Source: Prime Curios!

385

385 = 5 x 7 x 11.

385 is the number of integer partitions of 18.

385 is a square pyramidal number (the sum of the squares of all integers from 1 to 10).

385 is a Cullen number.

385 = 193² - 192².

385 is 1441 in base 6 and 181 in base 18.

Source: What's Special About This Number?

193

193 is a prime number.

191 and 193 form a twin prime pair.

193 can be formed from the sum of the products of the first three twin prime pairs: 193 = 3 * 5 + 5 * 7 + 11 * 13.

193 can be written as the difference between the product and the sum of the first four primes: 193 = 2 * 3 * 5 * 7 - (2 + 3 + 5 + 7).

193 is the smallest prime whose reversal is a Smith number.

193 is the smallest prime whose fifth power (267785184193) contains all the digits from 1 to 9.

193 has a representation as a sum of two squares: 193 = 7² + 12².

193 is the hypotenuse of a primitive Pythagorean triple: 193² = 95² + 168².

Source: Prime Curios!

569

569 is a prime number.

569 and 571 form a twin prime pair. The 569th and 571st Fibonacci numbers are also primes.

569 = 9² + 8² + 7² + 6² + 5² + 4² + 3² + 2² + 1² + 2² + 3² + 4² + 5² + 6² + 7² + 8² + 9².

569 is 2345 in base 6.

569 has a representation as a sum of two squares: 569 = 13² + 20².

569 is the hypotenuse of a primitive Pythagorean triple: 569² = 231² + 520².

Source: Prime Curios!

449

449 is a prime number.

449 is the smallest prime number whose digits are composite perfect squares. It is also the smallest prime number that can be constructed from two concatenated prime squares: 2² and 7². And it is the smallest prime whose digits are all semiprimes.


449 is the 87th prime. Note that 4² + 4² + 9² = 8² + 7² = 113.


449 is the sum of five consecutive prime numbers: 449 = 79 + 83 + 89 + 97 + 101.

449 has a representation as a sum of two squares: 449 = 7² + 20².

449 is the hypotenuse of a primitive Pythagorean triple: 449² = 280² + 351².

Source: Prime Curios!

932

932 = 2 x 2 x 233.

932 has a representation as a sum to two squares: 932 = 16² + 26².

932 is the maximum number of regions into which 31 circles divide the plane.

932 is the number of permutations of length 9 within distance 2 of a fixed permutation (A002524).

932 is the sum of five distinct positive pentatope numbers (A104396).

Source: On-Line Encyclopedia of Integer Sequences

1305

1305 = 3 x 3 x 5 x 29.

1305 has two representations as a sum of two squares: 1305 = 3² + 36² = 24² + 27².

1305 is the number of graphs with 11 vertices and 9 edges.

1305 is 909 in base 12.

1305 is a number n such that n² (1703025) can be obtained by inserting internal (but not necessarily contiguous) digits (A046851).

Source: What's Special About This Number?

6115

6115 = 5 x 1223.

6115 is a number n such that n² - 6 and n² + 6 are both prime (A108403).

6115 is the number of S, E, and NW-moving king's tours on a 13 x 13 board summed over all starting positions (A187510).

6115 Martinduncan is an asteroid discovered in 1984 and named in honor of astronomer Martin J. Duncan of Queen's University, Kingston, Ontario.

Source: On-Line Encyclopedia of Integer Sequences

624

624 = 2 x 2 x 2 x 2 x 3 x 13.

624 is 4444 in base 5. It is 1551 in base 7.

624 is the smallest number with the property that its first five multiples (624, 1248, 1872, 2496, 3120) contain the digit 2.

624 is the sum of twin primes: 624 = 311 + 313.

624 Hektor is the largest of the Jupiter Trojan asteroids.

Source: What's Special About This Number?

729

729 = 3 x 3 x 3 x 3 x 3 x 3 = 3⁶. It is a perfect sixth power.

729 is a centered octagonal number.

728 and 729 are consecutive Smith numbers, so they are known as Smith brothers.

729 is the smallest odd cube represented as the sum of two prime numbers: 729 = 2 + 727.

729 is a cube that is the sum of three cubes: 729 = 9³ = 1³ + 6³ + 8³.

729 = 27² = (1 + 2 + 2 + 2 + 4 + 4 + 4 + 8)² = 1³ + 2³ + 2³ + 2³ + 4³ + 4³ + 4³ + 8³.

729 is 1331 in base 8 and 121 in base 26.

Source: Prime Curios!

618

618 = 2 x 3 x 103.

618 = 0!² + 1!² + 2!² + 3!² + 4!².

618 is 4433 in base 5.

618 is the sum of 10 positive fifth powers (A003355): 618 = 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵ + 1⁵ + 1⁵ + 1⁵.

618 is the number of ternary squarefree words of length 15 (A006156).

Source: What's Special About This Number?

566

566 = 2 x 283.

566 is the number of ways to place 24 points on a 12 x 12 grid so that no three points are on a line (A000769).

The sum of the fourth power of the prime factors of 566 is a prime (A134620): 2⁴ + 283⁴ = 6414247937, a prime.

566 is the sum of five distinct pentatope numbers (A104395).

566 is the sum of the first 20 primes minus the next prime (A166448).

Source: What's Special About This Number?

409

409 is a prime number.

409 is a centered triangular number.

409 has a representation as a sum of two squares: 409 = 3² + 20².

409 is the hypotenuse of a primitive Pythagorean triple: 409² = 120² + 391².

409 is the smallest prime that, along with both its prime neighbors, uses non-prime digits: 401, 409, 419.

409 is the number of primes less than 10,000 that form members of twin prime pairs.

Source: Prime Curios!

815

815 = 5 x 163.

815 is a Lucas 3-step number.

815 is 3435 in base 6.

815² is the sum of three consecutive primes (A076304).

815 and 817 are both semiprimes (A136196).

Source: What's Special About This Number?

121

121 = 11 x 11.

121 is the smallest multidigit palindromic square. It is also the smallest palindromic composite such that some permutation of digits is prime. It is the only odd palindromic square with an odd number of digits that is divisible by a palindromic prime number with an even number of digits.

121 is a perfect square. It is also a centered octagonal number and a centered dodecagonal number.

Every number greater than 121 is the sum of distinct primes of the form 4n + 1.

121 is 11111 in base 3.

121 is the maximum number of regions into which 15 lines divide a plane.

121 can be expressed as the sum of a prime and its reversal for exactly three distinct primes: 121 = 29 + 92 = 47 + 74 = 83 + 38.

121 = 1 + 3¹ + 3² + 3³ + 3⁴.

121 is the number of points required to win a standard game of cribbage.

Source: Prime Curios!

802

802 = 2 x 401.

802 is the number of ways to toss a coin 10 times and not get a run of five (A135492).

802 has a representation as a sum of two squares: 802 = 19² + 21².

802 is 414 in base 14.

802 is the sum of eight consecutive primes (A127335): 802 = 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113.

802² is the sum of two consecutive primes (A074924): 802² = 643204 = 321593 + 321611.

802 is the number of isomers of the hydrocarbon chemical compound C₁₃H₂₈.

Source: On-Line Encyclopedia of Integer Sequences

401

401 is a prime number.

401 is the start of the first occurrence of three consecutive primes using no prime digits: 401, 409, 419.

401 is the sum of seven consecutive primes: 401 = 43 + 47 + 53 + 59 + 61 + 67 + 71. It is also the sum of nine consecutive primes: 401 = 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61.

401 is a divisor of 20⁴ - 1.

401 has a representation as a sum of two squares: 401 = 1² + 20².

401 is the hypotenuse of a primitive Pythagorean triple: 401² = 40² + 399².

401 was the hull number of the RMS Titanic.

Source: Number Gossip

783

783 = 3 x 3 x 3 x 29.

783 is a heptagonal number.

783 is the number of 11-ominoes that tile the plane by translation.

783³ = 480,048,687 = (48 + 00 + 48 + 687)³.

783 is 373 in base 15 and 234 in base 19.

Source: What Special About This Number?

679

679 = 7 x 97.

679 is the smallest number with multiplicative persistence 5 (A003001 and A064869).

679 is the sum of three consecutive primes: 679 = 223 + 227 + 229 (A034961). It is also the sum of nine consecutive primes (A127336): 679 = 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97.

679 is the sum of nine positive fifth powers (A003354): 679 = 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵.

The sum of the digits of 679 (6 + 7 + 9 = 22) exceeds the sum of the digits of 679² (4 + 6 + 1 + 0 + 4 + 1 = 17) (A064399).

Source: Number Gossip

494

494 = 2 x 13 x 19.

494 has the representation 494 = 2⁹ - 18.

The product of the first 494 composite numbers minus 1 is prime.

494 + 209 = 703 and 494,207 = 703².

494 is 3434 in base 5.

Source: Prime Curios!

868

868 = 2 x 2 x 7 x 31.

4⁸⁶⁸ - 3 is a prime number.

868 has a square root whose decimal part starts with the digits 1 to 9 in some order: 29.461839725. . .

868 is 4004 in base 6 (A029963).

868 is the number of ways of writing 60 as a sum of eight nonnegative cubes (A173681).

Source: Prime Curios!

396

396 = 2 x 2 x 3 x 3 x 11.

396 is a nonagonal number.

396 is the number of positions in a 3 x 3 sliding puzzle that require exactly 11 moves to solve starting with the hole in a corner.

396 is 112200 in base 3 and 1500 in base 6.

396 is the sum of a twin prime pair: 396 = 197 + 199.

396 refers to the displacement in cubic inches of early Chevrolet Big-Block engines.

Source: What's Special About This Number?

296

296 = 2 x 2 x 2 x 37.

296 is the number of integer partitions of 30 into distinct parts.

296 has a representation as a sum of two squares: 296 = 10² + 14².

296 x 333,667 = 98,765,432.

296 is 1212 in base 6.

Source: What's Special About This Number?

252

252 = 2 x 2 x 3 x 3 x 7.

252 is the smallest number that is the product of two distinct numbers that are reverse of each other: 252 = 12 x 21.

252 = 2⁸ - 4.

252 is the third value of Ramanujan's tau function (A000594).

252 is a hexagonal pyramidal number.

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 five heads and five tails.

Source: Number Gossip

574

574 = 2 x 7 x 41.

574 is the maximum number of pieces into which a torus can be cut by 14 slices.

574 is 210021 in base 3. It is 707 in base 9.

574 is the number of sevens among the digits of all four-digit primes (A152279).

574² = 329476 contains exactly six different digits (A054034).

Source: What's Special About This Number?

759

759 = 3 x 11 x 23. It is the product of three distinct Sophie Germain primes (A157346).

759 is 1001010 in base 3. It is 3303 in base 6 and 1033 in base 9 (and 2133 in base 7 and 533 in base 12).

759 is the sum of five consecutive primes (A034964): 759 = 139 + 149 + 151 + 157 + 163.

759 is a triangular matchstick number (A045943).

759 is the number of sets of natural numbers less than 37 that sum to 37 (A111133).

Source: On-Line Encyclopedia of Integer Sequences

662

662 = 2 x 331.

662 is a divisor of 31³ - 1.

662 is the index of the smallest triangular number that contains the digits 1, 2, 3, 4, and 5 (219,453).

662 is 220112 in base 3 and 22112 in base 4. It is 10122 in base 5 and 3022 in base 6.

662 is the sum of 12 consecutive primes (A127339): 662 = 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79.

Source: What's Special About This Number?

753

753 = 3 x 251.

753 is a divisor of 20¹⁰ - 1.

753 is the smallest composite number that you can get by concatenating all odd primes up to some number in decreasing order.

753 is the smallest number whose cube contains four consecutive sevens: 753³ = 426957777.

753 is 353 in base 15.

Source: Number Gossip

139

139 is a prime number.

137 and 139 form a twin prime pair.

139 is a divisor of 42³ - 1.

139 is the smallest prime that retains the end (unit) digit of its successor (149). 139 and 149 are the first consecutive primes differing by 10.

139 is the smallest prime with one prime digit, one composite digit, and one digit that is neither prime nor composite.

139 divides the sum of the first 139 composite numbers.

139 is the smallest prime number whose product of digits is a prime cube: 1 x 3 x 9 = 27 = 3³.

139 Juewa is a large, dark, main-belt asteroid discovered in 1874.

Source: Number Gossip

370

370 = 2 x 5 x 37.

370 is a decagonal number (A001107).

370/(3 + 7 + 0) = 37 is prime.

370 = 37 x (3 + 7) = 3³ + 7³. It is an Armstrong or narcissistic number (A005188) because it is equal to the sum of the cubes of its three digits.

370 is the average of the sum of all the possible permutations of its digits: (037 + 073 + 307 + 370 + 703 + 730)/6 = 370.

370 is the sum of four consecutive primes: 370 = 83 + 89 + 97 + 101.

370 has two representations as a sum of two squares: 370 = 3² + 19² = 9² + 17².

Source: Prime Curios!

946

946 = 2 x 11 x 43.

946 is the 43rd triangular number (A000217). It is the sum of all integers from 1 to 43.

946 is also a hexagonal number (A000384), a centered nonagonal number, and a hexagonal pyramidal number (A002412).

946 is the only three-digit number such that the reversal of the concatenation of the first 946 natural numbers is a prime.

946 is the largest known number n such that n is the sum of two consecutive primes but not the sum of two sums of two consecutive primes.

Source: Prime Curios!

224

224 = 2 x 2 x 2 x 2 x 2 x 7.

224 has a unique representation as a sum of three squares: 224 = 4² + 8² + 12².

224 is an abundant number (A005101).

The number 224 times 422 (its reversal) plus 1 and plus 3 are twin primes (94529 and 94531).

224 is an Entringer number (A008281).

224 is the sum of four consecutive cubes: 224 = 2³ + 3³ + 4³ + 5³.

There are 224 ounces in a stone (14 pounds).

Source: Prime Curios!

635

635 = 5 x 127.

635 is a number whose 5th root has a decimal part that begins with 635 (3.63542128. . .).

635⁴ = 162590400625, a concatenation of square numbers (16, 25, 9, 0, 400, 625).

635 is the sum of nine consecutive primes: 635 = 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89.

The sum of the digits of 635 is equal to the sum of the digits of the 635th prime (4703).

Source: What's Special About This Number?

732

732 = 2 x 2 x 3 x 61.

732 = 1⁷ + 2⁶ + 3⁵ + 4⁴ + 5³ + 6² + 7¹.

732 = 3⁶ + 3.

732 is a divisor of 13³ - 1.

732 is 444 in base 13. It is 606 in base 11.

Source: What's Special About This Number?

161

161 = 7 x 23.

161 is a divisor of 22² - 1.

161 is a hexagonal pyramidal number.

161 is a Cullen number.

Every number greater than 161 is the sum of distinct primes of the form 6n - 1.

161 is the smallest semiprime that yields a palindromic prime (191) when turned upside down.

161 is the sum of five consecutive prime numbers: 161 = 23 + 29 + 31 + 37 + 41.

There are 161 ways to bet on a roulette wheel.

Source: Prime Curios!