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!

722

722 = 2 x 19 x 19.

722 has a representation as a sum of two squares: 722 = 19² + 19².

722 is the sum of the fourth powers of the first three primes (A133531): 722 = 2⁴ + 3⁴ + 5⁴.

722 is the sum of two distinct factorials, the sum of the factorials of the digits of 26 (A061602): 722 = 2! + 6!

722 is the maximum number of regions into which the plane can be divided by 10 (concave) quadrilaterals (A077591).

Source: What's Special About This Number?

151

151 is a prime number.

149 and 151 form a twin prime pair.

151 is a centered decagonal number.

151 is the smallest palindromic prime sandwiched between two consecutive squareful (or non-squarefree) numbers.

151 is the smallest prime that begins a 3-run of sums of five consecutive primes: 151 + 157 + 163 + 167 + 173 = 811; and 811 + 821 + 823 + 827 + 829 = 4111, and 4111 + 4127 + 4129 + 4133 + 4139 = 20639. Can you find the smallest 4-run example?

The Statue of Liberty, from its base to the tip of its torch, was designed to be 151 feet tall.

Source: Prime Curios!

231

231 = 3 x 7 x 11. It is the 22nd number that is the product of three distinct primes.

231 is 11100111 in base 2 (binary).

231 is the number of integer partitions of 16.

231 is the 21st triangular number. It is the smallest triangular number in which the sum of the external digits equals the sum of the internal digits.

231 is a hexagonal number and an octahedral number.

231 = 2² + 3² + 7² + 13².

The U.S. liquid gallon is defined as 231 cubic inches.

Source: Number Gossip

913

913 = 11 x 83.

The integer digits of 913² = 833569 are exactly the same (albeit in a different order) as the integer digits of 914² = 835396 (A072841).

The digit sum of 913 equals the digit sum of its prime factors (A036920).

913 is a generalized polygonal number (A080859).

913 is the sum of the integers from 1 to 43, excluding perfect fifth powers (A132336).

Source: On-Line Encyclopedia of Integer Sequences

318

318 = 2 x 3 x 53.

The sum of the digits of 318 is one less than the sum of the digits of its prime factors.

318 is the number of unlabeled partially ordered sets of 6 elements.

318 is the sum of 12 consecutive primes: 318 = 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47.

318 is 2233 in base 5. It is 383 in base 9.

Source: Prime Curios!

523

523 is a prime number.

521 and 523 form a twin prime pair.

523 together with 541 form the smallest two consecutive primes such that the sums of their digits are equal. It is the smallest prime that is followed immediately by 17 composite numbers.

523 is the only three-digit prime containing all three of the first three prime digits. It is the largest prime with a prime number of distinct prime digits. It is the only prime formed from three consecutive primes, one being the sum of the other two.

523 is 313 in base 13.

523 is the sum of seven consecutive primes: 523 = 61 + 67 + 71 + 73 + 79 + 83 + 89.

Source: Number Gossip

1651

1651 = 13 x 127.

1651 is 11001110011 in base 2 (binary) (A048700).

1651 is a heptagonal number (A000566).

1651 is a potential magic constant of a 7 x 7 magic squares composed of consecutive primes (A188536).

1651 is the sum of eight but not fewer squared primes (A183215).

Source: On-Line Encyclopedia of Integer Sequences

7698

7698 = 2 x 3 x 1283.

7698² = 59259204.

7698 is the number of ways to place 10 non-attacking kings on a 4 x 10 chessboard (A061593).

The set of base 7 digits of 7698 equals the set of base 9 digits of 7698 (A037439): {0, 1, 3, 5}.

7698 is a number n for which 12n + 1, 12n + 5, 12n + 7, and 12n + 11 are primes (A123985).

Source: On-Line Encyclopedia of Integer Sequences

765

765 = 3 x 3 x 5 x 17.

765 has two representations as a sum of two squares: 765 = 6² + 27² = 18² + 21².

765 = 401 + 263 + 89 + 7 + 5. Its reversal, 567, is the smallest number that is the sum of different primes using all ten digits.

765 is 1011111101 in base 2 (A006995) and 636 in base 11.

765 is the sum of eight positive fifth powers (A003353): 765 = 3⁵ + 3⁵ + 3⁵ + 2⁵ + 1⁵ + 1⁵ + 1⁵ + 1⁵.

Source: Prime Curios!

204

204 = 2 x 2 x 3 x 17.

204 is 11001100 in base 2 (binary).

204 is a nonagonal number and a square pyramidal number. It is also an abundant number.

The number 204ⁿ + 1 is prime for n = 2, 0, and 4.

204 is the square root of the triangular number 41616.

204² = 23³ + 24³ + 25³ = 41616.

204 is the sum of twin primes: 204 = 101 + 103.

204 is the number of different squares that you can find on a standard chessboard.

Source: Number Gossip

1518

1518 = 2 x 3 x 11 x 23.

1518 is a divisor of 47¹⁰ - 1.

1518 is the sum of its proper divisors that contain the digit 5: 1518 = 253 + 506 + 759.

1518 is the sum of two consecutive sums of consecutive numbers: 1518 = 121 + 122 + . . . + 131 + 132 = 133 + 134 + . . . + 142 + 143.

1518 is 2002020 in base 3. It is 330 in base 22.

Source: What's Special About This Number?

758

758 = 2 x 379.

758 is the maximum number of regions into which 28 circles divide the plane.

758 is 464 in base 13 and 262 in base 18.

758 is the number of walks on a cubic 4 x 4 x 4 lattice (starting at the origin and not going below the x-y plane) (A005573).

758 is the smallest of three consecutive integers (758, 759, 760) divisible by three consecutive primes respectively (2, 3, 5) (A073607).

Source: On-Line Encyclopedia of Integer Sequences

391

391 = 17 x 23.

391 is a Smith number (A0906753). The sum of its digits (3 + 9 + 1 = 13) equals the sum of the digits of its prime factors (1 + 7 + 2 + 3 = 13).

391 is a centered pentagonal number (A005891).

391 is 474 in base 9 (A029955).

391 is a substring of 2³⁹¹ (A032740).

391, 393, and 395 are all semiprimes (A092125), between the prime numbers 389 and 397.

Source: On-Line Encyclopedia of Integer Sequences

473

473 = 11 x 43.

473 is the largest known number whose square (223729) and fourth power (50054665441) use different digits (and no digit 8).

473 x 8 = 3784 (same digits are used on both sides).

473 is 575 in base 9.

473 is the sum of five consecutive primes (A034964): 473 = 83 + 89 + 97 + 101 + 103.

473 is the number of ways of making change for 51 cents using coins of 1, 2, 5, 10, 20, and 50 cents (A001313).

Source: What's Special About This Number?

965

965 = 5 x 193.

965 has two representations as a sum of two squares: 965 = 2² + 31² = 17² + 26²
(A088909).

965 is the hypotenuse of two primitive Pythagorean triples (A024409): 965² = 124² + 957² = 387² + 884² (A165158).

Both 965 and 965² = 931225 have the same initial digit and the same final digit (A086457).

965 is the number of unit squares at least 50% covered by a circle inscribed in an integer square of size 35 x 35 (A051233).

Source: On-Line Encyclopedia of Integer Sequences

1400

1400 = 2 x 2 x 2 x 5 x 5 x 7.

1400 is a divisor of 99² - 1.

1400 is the number of different arrangements of 4 non-attacking queens on a 4 x 10 chessboard (A061990).

1400 is 4040 in base 7.

1400 is divisible by the square of the sum of its digits (25) (A072081).

1400 is the sum of the digits in the 41st row of Pascal's triangle (A066600).

Source: What's Special About This Number?

656

656 = 2 x 2 x 2 x 2 x 41.

656 is 1010010000 in base 2 (binary). It is a palindrome in base 3 (220022) (A007633 and A014190), base 9 (808), and base 10 (656) (A029965).

656 has a representation as a sum of two squares: 656 = 16² + 20².

656 has 10 binary digits and 10 divisors (1, 2, 4, 8, 16, 41, 82, 164, 328, 656) (A135772).

656 plus the 656th prime produces a triangular number (A115882): 656 + 4909 = 5565.

Source: What's Special About This Number?

848

848 = 2 x 2 x 2 x 2 x 53.

848 has a representation as a sum of two squares: 848 = 8² + 28².

848 is the number of inequivalent binary linear codes of length 9.

848 is the sum of the first 33 nonprimes (A051349).

848 is the sum of distinct factorials (A059590): 848 = 6! + 5! + 3! + 2!

Source: What's Special About This Number?

938

938 = 2 x 7 x 67.

938 is the number of lines passing through at least two points of an 8 x 8 grid of points (A018808).

938 is the total number of positive integers below 10⁵ requiring two positive cubes in their representation as a sum of cubes (A181375).

938 is the smallest of three consecutive integers (938, 939, 940) divisible by three consecutive primes respectively (2, 3, 5) (A073607).

938 is the sum of two consecutive primes and all the composite numbers in between (A174518): 938 = 131 + 132 + 133 + 134 + 135 + 136 + 137.

Source: What's Special About This Number?

191

191 is a prime number. It is a Sophie Germain prime because 2 x 191 + 1 = 383 is also a prime. In addition, the resulting number is a palindrome.

191 and 193 form a twin prime pair.

191 is the maximum number of regions into which 19 lines divide the plane.

191 is the smallest palindromic prime whose digit sum (1 + 9 + 1 = 11) is a multidigit palindromic prime. It is also the smallest multidigit palindromic prime that yields a palindrome when multiplied by the next prime: 191 x 193 = 36863.

191 is the smallest prime in a set of four consecutive primes (191, 193, 197, 199) whose sum of digits is another set of four primes (11, 13, 17, 19).

The common U.S. coins--a silver dollar, half-dollar, quarter, dime, nickel, and penny--add up to 191 cents.

Source: Number Gossip

185

185 = 5 x 37.

185 has two representations as a sum of two squares: 185 = 4² + 13² = 8² + 11².

185 is the hypotenuse of two primitive Pythagorean triples: 185² = 57² + 176² = 104² + 153².

185 is the number of conjugacy classes in the automorphism group of the 8-dimensional hypercube.

185 is 505 in base 6 and 353 in base 7.

NGC 185 is a dwarf elliptical galaxy in the constellation Cassiopeia.

Source: What's Special About This Number?

274

274 = 2 x 137.

274 has a representation as a sum of two squares: 274 = 7² + 15².

274 is a centered triangular number.

274 is the maximum number of regions into which 17 circles divide the plane.

(274 - 2)² + (274 - 7)⁷ + (274 - 4)⁴ is a prime.

The 274th Lucas number plus 274 is a prime.

274 is the sum of five positive cubes: 274 = 3(2³) + 2(5³).

Source: Prime Curios!

1375

1375 = 5 x 5 x 5 x 11.

1375 is a decagonal pyramidal number (A007585).

1375 is 111133 in base 4.

1375 is the smaller of two consecutive numbers each divisible by a cube (A068140). It is also the smallest of three consecutive numbers divisible by a square (A070258).

1375² = 1,890,625 contains exactly seven different digits (A054035).

Source: What's Special About This Number?

735

735 = 3 x 5 x 7 x 7. It is a number divisible by the product of its digits (A007602). It is also divisible by the sum of its digits (7 + 3 + 5 = 15) (A038186).

735 is the smallest number that is the concatenation of its distinct prime factors.

735 is 3223 in base 6 (A029953).

735 is the sum of nine positive fifth powers (A003354): 735 = 3⁵ + 3⁵ + 3⁵ + 1⁵ + 1⁵ + 1⁵ + 1⁵ + 1⁵ + 1⁵.

Source: Number Gossip

723

723 = 3 x 241.

723 = (1!)! + (2!)! + (3!)! (A059590).

723 = 3⁶ - 6.

723 is 333 in base 15.

723 is the smallest positive number that can be written as a sum of distinct Fibonacci numbers in 25 ways (A013583).

723 is the sum of fifth powers of primes (A122616): 723 = 3⁵ + 15(2⁵).

Source: What's Special About This Number?

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?