407

407 = 11 x 37.

407 is a divisor of 100³ - 1.

407 is the maximum number of regions into which 28 lines divide the plane.

407 is the largest number that is the sum of the cubes of its digits: 407 = 4³ + 0³ + 7³. It is a narcissistic number.

407 = (7 - 3)³ + 7³.

407 is 1515 in base 6.

407 is the sum of three consecutive primes: 407 = 131 + 137 + 139.

Source: Number Gossip

182

182 = 2 x 7 x 13.

182 is a pronic number; it is the product of two consecutive numbers: 182 = 13 x 14.

182 is 222 in base 9 and 77 in base 25. It is 20202 in base 3 and 1212 in base 5.

182 is the number of connected bipartite graphs with 8 vertices.

182 = 3³ + 3³ + 4³ + 4³ = 14² - 14.

The USS Salmon  (SS-182) was a United States Navy submarine during World War II.

Source: Number Gossip

777

777 = 3 x 7 x 37.

777 is a divisor of 100³ - 1.

777 is 3333 in base 6.

Surrounding the number 777 with the number 11 forms the prime numbers 11777, 77711, 1177711, and 11117771111.

The Boeing 777 is a long-range, wide-body, twin-engine jet airliner.

Source: Numeropedia

869

869 = 11 x 79.

869 is the number of different resistances that can be created in a circuit of nine equal resistors (A048211).

The sum of the digits of 869 equals the sum of the digits of the 869th prime (6737) (A033549). 869 and the 869th prime (6737) have only the digit 6 in common (A107937).

869 is a number that yields a prime when 0 is inserted anywhere in it (but not added to the end or beginning) (A216169).

Source: What's Special About This Number?

2142

2142 = 2 x 3 x 3 x 7 x 17.

2142 is a divisor of 55⁴ - 1.

2142 is 32032 in base 5.

2142 is the sum of the totient function for the first 83 integers.

2142 is the number of ways of writing the number 63 as the sum of nine nonnegative cubes (A173682).

2142 is the sum of 10 consecutive primes (A127337): 2142 = 191 + 193 + 197 + 199 + 211 + 223 + 227 + 229 + 233 + 239.

Source: On-Line Encyclopedia of Integer Sequences

198

198 = 2 x 3 x 3 x 11.

198 is the smallest number with ten representations as a sum of four positive squares: 198 = 1² + 2² + 7² + 12² = 1² + 4² + 9² + 10² = 2² + 3² + 4² + 13² = 2² + 3² + 8² + 11² = 2² + 5² + 5² + 12² = 2² + 7² + 8² + 9² = 3² + 3² + 6² + 12² = 3² + 5² + 8² + 10² = 4² + 5² + 6² + 11² = 6² + 7² + 7² + 8².

198 is the first number between a twin prime pair such that if multiplied by its reversal (198 x 891 = 176418), the product is also between a twin prime pair.

198 can be formed by concatenating 19 and 8, where 19 is the 8th prime number. 198 is the (19 x 8 = 152)nd composite number.

198 = 11 + 99 + 88 = (100 - 1)(100-98).

198 x 27 = 5346 = 18 x 297. Each equality uses each of the nine digits 1 to 9 once.

Source: Prime Curios!

756

756 = 2 x 2 x 3 x 3 x 3 x 7.

756 is a pronic number, the product of two consecutive numbers, 27 and 28.

12 x 63 = 756 = 21 x 36.

756 is the maximum number of regions into which 14 spheres divide space.

756!/657! - 1 is a prime.

756 is 11011 in base 5. It is 3300 in base 6.

756 is the sum of six consecutive primes: 756 = 109 + 113 + 127 + 131 + 137 + 139.

Source: Number Gossip

387

387 = 3 x 3 x 43.

387 is the lesser of two consecutive numbers divisible by a square (A068781).

387 is 110000011 in base 2 (binary) (A006995).

387 x 7 - 38 = 2671, the 387th prime.

387 is the smallest number with sort-then-add persistence 10.

Source: Prime Curios!

667

667 = 23 x 29. It is the product of two successive primes (A006094) and two distinct Sophie Germain primes (A157344).

667 is the maximum number of regions into which 36 lines divide the plane (A000124).

667 is the number of asymmetric trees with 16 vertices (A000220).

667, 669, and 671 are all semiprimes (A092125).

667 YCF was on the license plates of the car driven by Meeno Paloma (Lou Diamond Philips) in the 2009 movie The Triangle.

Source: Prime Curios!

355

355 = 5 x 71.

355 divided by the prime number 113 yields a nice approximation of pi: 355/113 = 3.141592. . .

355 is the number of labeled topologies with four elements.

355 = 3 x 5! - 5.

355 is 543 in base 8 and 434 in base 9.

Source: Prime Curios!

740

740 = 2 x 2 x 5 x 37.

740 has two representations as a sum of two squares: 740 = 8² + 26² = 16² + 22².

740 is the number of self-avoiding walks of length 8.

740 is 3232 in base 8 and 345 in base 15.

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

Source: What's Special About This Number?

129

129 = 3 x 43.

129 is 10000001 in base (binary). It is 333 in base 6.

129 is the smallest number with four representations as a sum of three positive squares: 129 = 1² + 8² + 8² = 2² + 2² + 11² = 2² + 5² + 10² = 4² + 7² + 8².

129 is the sum of the first ten primes: 129 = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29.

129 is the smallest sum of distinct seventh powers: 129 = 1⁷ + 2⁷.

Source: Number Gossip

930

930 = 2 x 3 x 5 x 31. It is a pronic number, the product of two consecutive integers (A002378): 930 = 30 x 31. It is also the product of a prime and the previous number (A036689).

930 is the number of even permutations of seven elements with no fixed points.

930 is 656 in base 12 and 567 in base 13.

The sum of the divisors of 930 is a square (A006532): 1 + 2 + 3 + 5 + 6 + 10 + 15 + 30 + 31 + 62 + 93 + 155 + 186 + 310 + 465 + 930 = 2304 = 48².

Source: What's Special About This Number?

1124

1124 = 2 x 2 x 281.

1124 has a representation as a sum of two squares: 1124 = 10² + 32².

1124 is the maximum number of regions into which 34 circles divide a plane.

1124 is a number whose product of digits is equal to its sum of digits: 1 + 1 + 2 + 4 = 8 = 1 x 1 x 2 x 4.

1124 is 686 in base 13, 464 in base 16, 323 in base 19, and 272 in base 22.

1124 is a Leyland number (A076980).

Source: On-Line Encyclopedia of Integer Sequences

617

617 is a prime number.

617 and 619 form a twin prime pair.

617 = 1!² + 2!² + 3!² + 4!².

617 is the largest multi-digit prime that is exactly half of a number formed with distinct consecutive digits: 1234.

617 has a representation as a sum of two squares: 617 = 16² + 19².

617 is the hypotenuse of a primitive Pythagorean triple: 617² = 105² + 608².

617 is a divisor of 31¹¹ - 1.

Source: Prime Curios!

914

914 = 2 x 457.

914 has a representation as a sum of two squares: 914 = 17² + 25².

914 is the number of binary rooted trees with 15 vertices.

914 is 494 in base 14.

The sum of the digits of 914 (9 + 1 + 4 = 14) is a substring of 914 (A052018).

Each of the digits of 914 are squares (A046030).

Source: What's Special About This Number?

813

813 = 3 x 271.

813 are the first three digits of 813^e.

813 is 393 in base 15.

813 is a divisor of 99999 (A027893) and 9999999999 (A027895): 99999/813 = 123 and 9999999999/813 = 12300123.

813 is the concatenation of the sixth Fibonacci number and the sixth prime (A138821).

Source: What's Special About This Number?

7011

7011 = 3 x 3 x 19 x 41.

7011 yields a prime whenever 1 is inserted anywhere in the number (A068679 and A216165): 17011, 71011, and 70111 are all primes.

7011 is the sum of three cubes of distinct primes (A138853 and A138854): 7011 = 19³ + 5³ + 3³.

7011 is the number of 16-crossing knots with symmetry group Z2 (A052412).

7011 is the number of 5 x 5 arrays of squares of integers, symmetric about the main diagonal, with all rows summing to 36 (A156385).

Source: On-Line Encyclopedia of Integer Sequences

793

793 = 13 x 61.

793 is one less than twice its reversal: 793 = 2(397) - 1.

793 is a dodecagonal number and a centered dodecagonal number (A003154).

793 has two representations as a sum of two squares: 793 = 3² + 28² = 8² + 27².

793 is the hypotenuse of two primitive Pythagorean triples: 793² = 168² + 775² = 432² + 665².

Source: What's Special About This Number?

598

598 = 2 x 13 x 23.

598 is the largest number that is the sum of its first digit, the square of its second digit, and the cube of its third digit: 598 = 5¹ + 9² + 8³.

598 is 21112 in base 4. It is 4343 in base 5.

598 is a divisor of 47⁴ - 1.

598 is the maximum number of regions into which 13 spheres divide space.

Source: Number Gossip

787

787 is a prime number.

The six integers following 787 are divisible by the first six primes, respectively.

787 is the smallest prime that can be represented as the sum of a prime and its reversal in two different ways.

787 is 30103 in base 4, 656 in base 11, and 313 in base 16.

787 is the sum of five consecutive primes: 787 = 149 + 151 + 157 + 163 + 167.

The Boeing 787 Dreamliner is a long-range, mid-size, twin-engine jet airliner.

Source: Prime Curios!

254

254 = 2 x 127.

254 is the maximum number of regions into which 22 lines divide a plane. It is a central polygonal number (A000124).

254 is the smallest multi-digit composite number all of whose proper divisors include the digit 2.

254 is the sum of the first 13 semiprimes (A062198).

The state of Texas has 254 counties, the most of any state of the United States.

Source: What's Special About This Number?

403

403 = 13 x 31. It is the smallest semiprime whose factors form a pair of emirps (13 and 31).

403 is 110010011 in base 2.

403 has a unique representation as a sum of three squares: 403 = 3² + 13² + 15².

403 is a heptagonal number.

403 = 2³ + 3³ + 3³ + 5³ + 6³.

Source: Prime Curios!

305

305 = 5 x 61.

305 is the smallest odd composite that is the average of two consecutive Fibonacci numbers (233 and 377).

305 has two representations as a sum of two squares: 305 = 4² + 17² = 7² + 16².

305 is the hypotenuse of two primitive Pythagorean triples: 305² = 136² + 273² = 207² + 224².

305 is a divisor of 11⁴ - 1.

305 is the fifth hexagonal prism number. A hexagonal prism number has the form (n + 1)(n² + 3n + 1).

305 is 614 is base 7 and 461 in base 8.

Source: Prime Curios!

152

152 = 2 x 2 x 2 x 19.

152 = 8 x 19, where 19 is the eighth prime number.

152 is the smallest number that can be represented as the sum of the cubes of two distinct odd primes: 152 = 3³ + 5³.

152 is the largest known even number that can be expressed as the sum of two primes in exactly four ways.

152 has a square composed of the digits 0, 1, 2, 3, and 4: 152² = 23104.

152 is the sum of four consecutive primes: 152 = 31 + 37 + 41 + 43.

The USS Peterson (DE-152) was a destroyer escort in World War II.

Source: Prime Curios!

7613

7613 = 23 x 331.

7613 is a divisor of 85¹¹ - 1.

7613 is a number of the form 4n² - 3n + 1, for n = 44 (A054552).

7613 is a member of the sequence that results from starting with 1, reversing the digits, and adding 56 to get the next term (A118152).

7613 is a number n such that n² (57957769) contains no digit less than 5 (A175471).

Source: On-Line Encyclopedia of Integer Sequences

796

796 = 2 x 2 x 199.

796 is the sum of six consecutive primes (A127333): 796 = 113 + 127 + 131 + 137 + 139 + 149.

796 is the sum of eight positive fifth powers (A003353): 796 = 3⁵ + 3⁵ + 3⁵ + 2⁵ + 2⁵ + 1⁵ + 1⁵ + 1⁵.

796 is the number of ways to place three nonattacking knights on a 3 x 7 board (A172212).

796 is the sum of six distinct positive pentatope numbers (A104396).

796 is the number of unit square lattice cells enclosed by an origin-centered circle of radius 33 (A136485).

Source: On-Line Encyclopedia of Integer Sequences

575

575 = 5 x 5 x 23.

575 is a palindrome that is 1 less than a square (576 = 24²).

575 is 353 in base 13 (A029968).

575 is a centered octahedral number (A001845).

575 is the number of quadrilaterals that can be formed with perimeter 53 (in other words, partitions of 53 into four parts such that the sum of any three is more than the fourth) (A062890).

Source: What's Special About This Number?

860

860 = 2 x 2 x 5 x 43.

860 is the sum of four consecutive primes (A034963): 860 = 199 + 211 + 223 + 227.

860 is the sum of ten positive fifth powers (A003355): 860 = 3⁵ + 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵ + 1⁵ + 1⁵.

860 and 861 each have three distinct prime factors (A140077).

860 is the number of hexagons that can be formed with perimeter 35 (in other words, partitions of 35 into six parts such that the sum of any five is more than the sixth) (A069907).

Source: On-Line Encyclopedia of Integer Sequences

7463

7463 = 17 x 439.

7463 is 101020102 in base 3 (A043589) and 11212 in base 9 (A032930).

7463 is a number of the form n(13n - 3)/2 for n = 34 (A186030).

7463 is the number of primitive multiplex juggling sequences of length 6, base state <2>, and hand capacity 2 (A136782).

The 7463 Confidence is a product of the Singer Sewing Co.

Source: On-Line Encyclopedia of Integer Sequences

754

754 = 2 x 13 x 29.

754 has two representations as a sum of two squares: 754 = 5² + 27² = 15² + 23².

754 is a divisor of 57⁴ - 1.

754 is 626 in base 11. It is 3254 in base 6 and 354 in base 15.

754 is the sum of the first 31 nonprimes (A051349).

Source: On-Line Encyclopedia of Integer Sequences

230

230 = 2 x 5 x 23.

230 = 2 x 23 x (2 + 3) is the only number with prime factors produced simply from its first two digits, which happen to be the first two primes.

230 is the first number such that it and the next number (231 = 3 x 7 x 11) are both the product of three distinct primes.

230 is the sum of four consecutive squares: 230 = 6² + 7² + 8² + 9².

There are 230 crystal space groups, counting chiral copies as distinct.

Source: Prime Curios!

846

846 = 2 x 3 x 3 x 47.

846 has the property that its square is the concatenation of two consecutive numbers (A030467): 846² = 715716.

846 is 1516 in base 8.

846 is the sum of eight consecutive primes: 846 = 89 + 97 + 101 + 103 + 107 + 109 + 113 + 127.

846 is the sum of distinct factorials (A059590): 846 = 6! + 5! + 3!

Source: What's Special About This Number?

1271

1271 = 31 x 41.

1271 has a sixth power whose last eight digits are . . .21211121.

1271 is the sum of six positive fifth powers (A003351): 1271 = 4⁵ + 3⁵ + 1⁵ + 1⁵ + 1⁵ + 1⁵.

1271 is the sum of the first 40 composite numbers (A053767).

Marco Polo left Venice in the year 1271 to commence his travels in Asia.

Source: What's Special About This Number?

649

649 = 11 x 59.

649 is a semiprime whose digits are each a semiprime (A107342).

649 is the smallest number n so that n² is 1 more than 13 times a square: 649² = 1 + 13(180)².

649 is 345 in base 14.

649 is a brilliant number (A078972).

Gliese 649 is a red dwarf star in the constellation of Hercules.

Source: What's Special About This Number?

552

552 = 2 x 2 x 2 x 3 x 23.

552 is an oblong or pronic number (of the form n(n + 1)) (A002378): 552 = 23 x 24.

552 is the number of prime knots with 11 crossings (A002863).

552 is the sum of six consecutive primes: 552 = 79 + 83 + 89 + 97 + 101 + 103. It is also the sum of 10 consecutive primes: 552 = 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73.

552 is the sum of six positive fifth powers (A003351): 552 = 3⁵ + 3⁵ + 2⁵ + 2⁵ + 1⁵ + 1⁵.

The German submarine U-552, nicknamed "Red Devil," was in service during World War II.

Source: What's Special About This Number?

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?