1580

1580 = 2 x 2 x 5 x 79.

1580 is a divisor of 23¹² - 1.

1580 is a number n such that 1 + n + n³ + n⁵ + n⁷ + n⁹ + n¹¹ + n¹³ + n¹⁵ + n¹⁷ + n¹⁹ + n²¹ + n²³ is prime (A124181).

1580 is the number of regions in a 20-sided regular polygon that are four-sided polygons (4-gons) (A067151).

1580 is the number of partitions of 33² into distinct squares (A030273).

Source: On-Line Encyclopedia of Integer Sequences

562

562 = 2 x 281.

562!/265! - 1 is a prime.

562 is the maximum number of regions into which 33 lines divide a plane. 562 is also the maximum number of regions a circle can be cut into by joining 11 points on the circumference with straight lines.

562 is the sum of 12 consecutive primes: 562 = 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71.

562 is a Smith number.

562 has a representation as a sum of two squares: 562 = 11² + 21².

Source: Prime Curios!

978

978 = 2 x 3 x 163.

978 = 2⁴ + 3⁴ + 4⁴ + 5⁴.

The sum of the digits of 978 equals the number of digits times 8 (A061425).

978 is the least sum of four nonzero squares in exactly 45 ways (A025416).

978 is the sum of ten positive fifth powers (A003355).

978 is the number of ways to place a six nonattacking kings on a 5 x 5 chessboard (A172158).

Source: What's Special About This Number?

588

588 = 2 x 2 x 3 x 7 x 7.

588 is the number of possible rook moves on a 7 x 7 chessboard.

588 is a Smith number (A006753); the sum of its digits is equal to the sum of the digits of its prime factors: 5 + 8 + 8 = 2 + 2 + 3 + 7 + 7 = 21.

588 is a composite number such that the cube root of the sum of the cubes of its prime factors is an integer (A134608): 2³ + 2³ + 3³ + 7³ + 7³ = 729 = 9³.

588 is a composite number divisible by the sum of its prime factors (21) (A046346).

588 is the number of ways of writing 30 as the sum of nine nonnegative cubes (A173682).

Source: What's Special About This Number?

817

817 = 19 x 43.

817 is a centered hexagonal (hex) number (A003215).

817 is the sum of three consecutive prime numbers: 817 = 269 + 271 + 277.

817 has the representation 817 = 3⁶ + 88.

The sum of the even digits of 817 equals the sum of the odd digits of 817 (A036301).

817 is a number n such that 1 + n² + n⁴ + n⁶ + n⁷ is a prime (A126908).

Source: On-Line Encyclopedia of Integer Sequences

1636

1636 = 2 x 2 x 409.

1636 is 11001100100 in base 2 (binary).

1636 appears inside its fourth power: 1636⁴ = 7,163,630,838,016.

1636 has a representation as a sum of two squares: 1636 = 40² + 6².

1636 is the total number of parts in all partitions of 36 into prime parts (A084993).

Source: What's Special About This Number?

399

399 = 3 x 7 x 19.

399 is 333 in base 11.

399 is the total number of parts in all partitions of 12.

399 is the smallest Lucas-Carmichael number.

399 = 7¹ + 7² + 7³.

399 is the smallest number, all of whose prime factors are of the form 4n + 3, whose sum of distinct prime factors is prime (3 + 7 + 19 = 29).

399 is the sum of 11 consecutive primes: 399 = 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59.

Source: Number Gossip

608

608 = 2 x 2 x 2 x 2 x 2 x 19.

608 is a number that has no digits in common with its cube (224,755,712).

608 is 211112 in base 3 (A014190).

608 is the number of 3 x 3 magic squares (with distinct positive entries) having all entries less than 21 (A108576).

608 is the smallest of three consecutive integers (608, 609, 610) divisible by three consecutive primes, respectively (A073607).

Source: What's Special About This Number?

906

906 = 2 x 3 x 151.

906 is the number of perfect graphs with 7 vertices.

906 = 2⁵ x 3³ + 42.

906 is an even number that is not the sum of a pair of twin primes (A007534).

906 is a number n such that the concatenation 2n3n5n7n11n13 is a prime (A092117).

906 is a strobogrammatic cyclops number (A153806).

Source: What's Special About This Number?

1474

1474 = 2 x 11 x 67.

1474 is a member of a Fibonacci-like sequence starting with 2 and 9.

1474 is the difference between the product of two consecutive primes and the next prime (A111071).

1474 has the property that all pairs of consecutive digits differ by 3 (A033081).

1474 is pandigital in Roman numerals (MCDLXXIV). It uses each of the symbols I, V, X, L, C, and M at least once (A105417).

Source: What's Special About This Number?

690

690 = 2 x 3 x 5 x 23.

690 is the smallest number that can be written as the sum of a triangular number, a cube, and a Fibonacci number.

690 is the sum of six consecutive primes: 690 = 103 + 107 + 109 + 113 + 127 + 131.

690 has the representation 690 = 3⁶ - 39.

690 is a divisor of 91² - 1.

Source: What's Special About This Number?

1337

1337 = 7 x 191.

1337 is a number with exactly two palindromic prime factors and no other prime factors (A046368).

1337 is the smallest number m such that reversal of m¹⁰⁰⁰ is prime.

1337 is a multiple of 7 such that its digit sum (1 + 3 + 3 + 7 = 14) is divisible by 7 (A216994).

1337 is the product of two distinct primes a and b such that a + b is the average of a twin prime pair (A176875): 7 + 191 = 198 = (197 + 199)/2.

1337 is the average of three successive primes, each squared (A075893).

1337 is a multiple of 7 containing only odd digits (A061825).

1337 is a divisor of 39¹⁵ - 1.

1137 Gerarda is an asteroid discovered in 1934.

Leet (or "1337") is an alternative alphabet for the English language that is used mainly on the Internet.

Source: Number Gossip

862

862 = 2 x 431.

862 is a number whose sum of divisors is a fourth power: 1 + 2 + 431 + 862 = 1296 = 6⁴.

862 is the maximum number of regions into which 41 lines divide the plane.

862 has the representation 862 = 2⁵ x 3³ - 2.

862 is a divisor of 95⁵ - 1.

Source: What's Special About This Number?

2220

2220 = 2 x 2 x 3 x 5 x 37.

2220 is a divisor of 31⁴ - 1.

2220 is a multiple of six and the sum of its digits is also six (A062768).

2220 is the sum of even numbers in the range 440 to 449 (A053741).

2220 is the number of partitions of 3⁶ into powers of 6 (A196884).

2220 is a year in which the month of February has five Tuesdays (A143994).

Source: On-Line Encyclopedia of Integer Sequences

1401

1401 = 3 x 467.

1401, 1402, and 1403 are each the product of two primes (semiprimes) (A056809). 1401, 1403, and 1405 are each the product of two primes (A092125).

1401 is a composite number such that every concatenation of its prime factors (3467 and 4673) is prime (A217263).

1401 is the number of 8-digit primes that can be represented as sums of consecutive squares (A218213).

1401 in base 6 (10253) has five distinct digits (A031983).

Source: On-Line Encyclopedia of Integer Sequences

761

761 is a prime number. It is a Sophie Germain prime because 2 x 761 + 1 = 1523 is also prime.

761 is a centered square number.

761 is the sum of all primes numbers up to 79.

761 has a representation as a sum of two squares: 761 = 19² + 20².

761 is the hypotenuse of a primitive Pythagorean triple: 761² = 39² + 760².

A sequence of six nines (known as the Feynman point) begins immediately after the 761st decimal place of pi. Physicist Richard Feynman expressed a wish to memorize the digits of pi as far as that point so that when reciting them he would be able to end with ". . . nine, nine, nine, nine, nine, nine, and so on."

Source: Prime Curios!

341

341 = 11 x 31.

341 is 101010101 in base 2 (binary). It is 11111 in base 4.

341 is an octagonal number and a centered cube number.

341 is the first composite number to disprove an ancient Chinese conjecture (circa 500 B.C.) that n is a prime number if and only if n divides the number 2ⁿ - 2. The number 2³⁴¹ - 2 is divisible by 341, a composite number. 341 is the smallest pseudoprime in base 2.

341 is the sum of seven consecutive primes: 341 = 37 + 41 + 43 + 47 + 53 + 59 + 61.

341 = 4⁰ + 4¹ + 4² + 4³ + 4⁴.

341 is the smallest number with seven representations as a sum of three positive squares: 341 = 1² + 4² + 18² = 1² + 12² + 14² = 2² + 9² + 16² = 4² + 6² + 17² = 4² + 10² + 15² = 6² + 7² + 16² = 8² + 9² + 14².

Source: Number Gossip

734

734 = 2 x 367.

734 is the smallest number that can be written as the sum of three distinct non-zero squares in ten ways.

734 is the sum of eight positive fifth powers (A003353).

734 is the number of hexagons that can be formed with perimeter 34 (A069907).

734 is the sum of 14 but no fewer nonzero fourth powers (A046045).

734 has the representation 734 = 3⁶ + 5.

734 is a divisor of 83³ - 1.

Source: What's Special About This Number?

971

971 is a prime number.

971 is the largest prime containing only odd digits, in decreasing order.

971 is the largest prime formed from the concatenation of a one-digit composite number, one-digit prime number, and one-digit number that is neither prime nor composite.

971, 719, and 197 are all primes.

971 is the smallest of three consecutive primes with a difference of six; a prime p such that p (971), p + 6 (977), and p + 12 (983) are all primes (A047948).

Source: Prime Curios!

5038

5038 = 2 x 11 x 229.

5038 is the sum of two distinct prime cubes (A120398): 5038 = 17³ + 5³.

5038 is the least nontrivial multiple of the 50th prime (229) beginning with 5 (A078289).

5038 is a number n such that n² (25381444) ends in 444 (A039685).

5038 is the difference of between two factorial numbers (A051949).

Source: On-Line Encyclopedia of Integer Sequences

556

556 = 2 x 2 x 139.

556 is the total number of parts in all partitions of 13.

556 are the first three digits of 4⁵⁵⁶.

556 is the sum of four consecutive primes: 556 = 131 + 137 + 139 + 149.

556 is an untouchable number; it is never the sum of the proper divisors of any integer.

556 Phyllis is an asteroid orbiting the sun, discovered in 1905.

U-556 was a German submarine that was built for and operated during World War II.

Source: What's Special About This Number?

1771

1771 = 7 x 11 x 23.

1771 is the smallest of three consecutive numbers that are products of exactly three primes (A113789).

1771 is the 21st tetrahedral number (A000292).

1771 is the concatenation of the 7th prime (17) and its reverse (71) (A067087).

1771 is a divisor of 45⁶ - 1.

1771 is a number n such that n² (3136441) is a concatenation of two nonzero squares (A048375): 3136 = 56² and 441 = 21².

Source: Number Gossip

1573

1573 = 11 x 11 x 13.

1573 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

1573 is a number n for which 10n + 1, 10n + 3, 10n + 7, and 10n + 9 are primes (A007811).

1573 is the sum of the remainders when the 48th prime (223) is divided by primes up to the 47th prime (211) (A033955).

1573 is a concentric tridecagonal number (A195045).

1573 is a divisor of 27⁵ - 1.

1573 has a representation as a sum of two squares: 1573 = 22² + 33².

Source: What's Special About This Number?

585

585 = 3 x 3 x 5 x 13.

585 is 1001001001 in base 2 (binary) and 1111 in base 8. It is a palindrome in base 2, base 8, and base 10.

585 is the number of integer partitions of 35 into distinct parts.

585 has two representations as a sum of two squares: 585 = 3² + 24² = 12² + 21².

585 is a divisor of 64² - 1.

Source: What's Special About This Number?

9966

9966 = 2 x 3 x 11 x 151. It has exactly four distinct palindromic prime factors (A046402).

9966 is the largest four-digit strobogrammatic number (A000787).

9966 is a number m such that (6 x m)⁵ is a sum of a twin prime pair (A173560).

9966 is an integer of the form 1/3 + 2/3 + 3/3 + 5/3 + 7/3 + 11/3 + 13/3 + 17/3 + ... (A182155).

Source: What's Special About This Number?

984

984 = 2 x 2 x 2 x 3 x 41.

984 is a divisor of 83² - 1.

984 = 8 + 88 + 888.

984 is a number n such that 1 + n + n³ + n⁵ + n⁷ + . . . + n²³ + n²⁵ + n²⁷ is a prime (A124185).

984 are the final three digits of 2⁵⁴ (A126605).

Source: What's Special About This Number?

470

470 = 2 x 5 x 47.

470 is a cake number, the maximum number of pieces into which a cylindrical cake can be cut with 14 straight-plane cuts (A000125).

470 has a base 3 representation (122102) that ends with its base 6 representation (2102).

470 is the sum of the first 24 non-primes (A051349).

470 is a number n such that its square (220900) is a sum of two successive primes (A074294).

Source: Number Gossip

1534

1534 = 2 x 13 x 59.

1534 is 4321 in base 7.

1534 arises in the sequence generated by starting with 1 then successively doubling the number and adding 1 to the result (A083416).

1534 has exactly nine 1s in its binary expansion (A023961).

1534 is the sum of the first 37 primes minus the sum of the first 37 non-primes (A071411).

Source: What's Special About This Number?

896

896 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7.

896 has a unique representation as a sum of three squares: 896 = 8² + 16² + 24².

896 cannot be expressed as a sum of four non-zero squares.

896 is the sum of six consecutive primes: 896 = 137 + 139 + 149 + 151 + 157 + 163.

896 is the numerical equivalent of the word TWO on a touch-tine telephone.

896 is the number of different moves a rook can make on a chessboard.

Source: Number Gossip

795

795 = 3 x 5 x 53.

795 is a number whose sum of divisors is a fourth power (A006532): 1 + 3 + 5 + 15 + 53 + 159 + 265 + 795 = 1296 = 6⁴.

795 is the smallest multiple of 5 with a digit sum of 21 (A069534).

795 is the sum of seven positive fifth powers (A003352).

795 is a divisor of 23⁴ - 1.

795 has the representation 795 = 3⁶ + 66.

Source: What's Special About This Number?

969

969 = 3 x 17 x 19.

969 and 970 have three distinct prime factors (A140077).

969 is the 17th tetrahedral number (A000292). It is the smallest multidigit tetrahedral palindrome.

969 is a nonagonal number (A001106).

The 18th Mersenne prime has 969 digits (A028335).

The sum of the digits of 969 equals the number of digits times 8 (A061425).

Source: Number Gossip

2181

2181 = 3 x 727. It is an odd number with two distinct palindromic prime factors (A046404).

2181, 2182, and 2183 are each the product of two primes (semiprimes) (A056809).

The sum of 2181 and the 2181st prime (19,231) produces a palindrome (A115884): 2181 + 91231 = 21412.

2181 is the maximum length of a non-crossing path on a 34 x 34 square lattice (A049486).

2181 has the representation 2181 = 3⁷ - 1.

2181 is a divisor of 46¹¹ - 1.

Source: On-Line Encyclopedia of Integer Sequences

786

786 = 2 x 3 x 131. It is the product of three distinct Sophie Germain primes (A157346).

786 is a number n such that n² (617796) has the property that the sum of its digits (36 = 6²) and the product of its digits are nonzero squares (A061268).

786 is an even number that is not the sum of a pair of twin primes (A007534).

786 and the 786th prime (6029) have only the digit 6 in common (A107937).

786 is the sum of six positive cubes in exactly three ways (A048931).

Source: On-Line Encyclopedia of Integer Sequences

337

337 is a prime number.

337 is a centered dodecagonal number.

81³ + 162³ = 9⁷.

337 has a representation as a sum of two squares: 337 = 9² + 16².

337 is the hypotenuse of a primitive Pythagorean triple: 337² = 175² + 288².

337 is a divisor of 8⁷ - 1.

Source: Prime Curios!

864

864 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3.

864 is the number of integer partitions of 38 into distinct parts.

864 is the sum of a twin prime pair: 864 = 431 + 433.

864 is the sum of six consecutive prime numbers: 864 = 131 + 137 + 139 + 149 + 151 + 157.

864 is a concentric hexagonal number (A032528).

Source: What's Special About This Number?

963

963 = 3 x 3 x 107.

963 is the sum of the first 24 primes (A007504). It is the smallest composite number that is a sum of 24 distinct primes (A073619).

963 is a number n such that the digits of n² (927369), reversed, include the digits of n as a substring (A115761).

963 and 964 both have six divisors (A049103).

963 is the sum of two consecutive semiprimes (A173966): 963 = 478 + 485.

Source: On-Line Encyclopedia of Integer Sequences

398

398 = 2 x 199.

398 is the number of integers with integer complexity 22.

398 is the solution to the postage problem with two denominations and 37 stamps (A014616).

398 is a number n such that n¹⁰ + n⁹ + n⁸ + n⁷ + n⁶ + n⁵ + n⁴ + n³ + n² + n + 1 is prime (A162862).

398 is the smallest even number with digit sum 20 (A069532).

398 and the 398th prime (2729) have only the digit 9 in common (A107940).

Source: What's Special About This Number?

1446

1446 = 2 x 3 x 241.

1446 is 666 in base 15.

1446 is the number of graphs with with 9 vertices and 5 edges.

1446 is the squarefree sum of two successive primes (A206329): 1446 = 719 + 727.

1446 is a number n such that 1 + n + n³ + n⁵ + n⁷ + n⁹ + n¹¹ + n¹³ is a prime (A124164).

Source: What's Special About This Number?

1386

1386 = 2 x 3 x 3 x 7 x 11.

1386 is the smallest number n such that n and 6n (6 x 1386 = 8316) are anagrams.

1386 = 1 + 3⁴ + 8 + 6⁴.

1386 is an octagonal pyramidal number (A002414).

1386 is the number of ways of writing 59 as a sum of 9 nonnegative cubes (A173682).

Source: Number Gossip

2007

2007 = 3 x 3 x 223.

2007 divides the sum of the digits of 2²⁰⁰⁷ x 2007!

2007 is a number n such that 25n +1 is a square (A219259).

The sum of the base 2 digits of 2007 (1 + 1 + 1 + 1 + 1 + 0 + 1 + 0 + 1 + 1 + 1 = 9) equals the sum of the base 10 digits of 2007 (2 + 0 + 0 + 7 = 9) (A037308).

2007 is a pentadecagonal number (A051687).

2007 is the smallest of three consecutive numbers, each divisible by a square (A070258).

Source: What's Special About This Number?

721

721 = 7 x 103.

721 is a centered hexagonal number (A003215).

721 is the smallest number that can be written as the difference of two positive cubes in two ways (A014440).

721 is the sum of nine consecutive primes: 721 = 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101.

721 is the sum of the factorials of the digits of 16 (A061602): 721 = 6! + 1!

Source: What's Special About This Number?

1080

1080 = 2 x 2 x 2 x 3 x 3 x 3 x 5.

1080 is a pentagonal number (A000326).

1080 is the smallest number with 18 divisors. The sum of the divisors of 1080 is a square (A006532).

1080 is the sum (in degrees) of the internal angles of an eight-sided polygon.

1080 is a number that can be expressed as the difference of the squares of primes in just two distinct ways (A090788).

Source: What's Special About This Number?

708

708 = 2 x 2 x 3 x 59.

708 is the maximum value of n so that there exist four denominations of stamps so that every postage from 1 to n can be paid for with at most 12 stamps (A001209).

708 is a decagonal pyramidal number (A007585).

708 is the number of different equations that can be made by summing numbers from 1 to 10 and using every number not more than once (A161943).

708 is the sum of the first 29 composite numbers (A053767).

Source: What's Special About This Number?

838

838 = 2 x 419. It is a palindrome with exactly two prime factors (A046328). Both prime factors are distinct Sophie Germain primes (A157344). The sum of its prime factors is a prime (A108605): 2 + 419 = 421.

838 is a happy number.

838 and 838² = 702244 have the same digit sum (A058369).

838 is the number of primes between 140,000 and 150,000 (A038824).

838 is the integer part of the surface area of a regular tetrahedron with edge length 22 (A171972).

Source: On-Line Encyclopedia of Integer Sequences

1744

1744 = 2 x 2 x 2 x 2 x 109.

1744 has a representation as a sum of two squares: 1744 = 12² + 40².

1744 is a divisor of 33⁴ - 1.

1744 is a multiple of 8 that has a digit sum that is a multiple of 8 (A216997).

1744 is a non-palindromic balanced number: the sum of its first two digits equals the sum of its last pair of digits (A145808).

Source: On-Line Encyclopedia of Integer Sequences

583

583 = 11 x 53.

583 is the sum of the first 27 nonprimes (A051349).

583 is the first integer n such that 47 x 2ⁿ + 1 is prime.

583 is the least integer that is not a sum or difference of two integers such that all their prime factors are 2, 3, and 5.

583 is the smallest number whose reciprocal has period 26.

583 is the sum of six positive fifth powers: 583 = 3⁵ + 3⁵ + 2⁵ + 2⁵ + 2⁵ + 1⁵.

Source: Prime Curios!

1543

1543 is a prime number.

1543 = 1111 + 55 + 44 + 333.

1543 is the sum of five positive fifth powers (A003350): 1543 = 4⁵ + 3⁵ + 3⁵ + 2⁵ + 1⁵.

1543 is the sum of 11 consecutive primes (A127338): 1543 = 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167.

1543 is a prime sandwiched between two numbers (1542 and 1544) having the same number of divisors (A067889).

The Köstritzer brewery in Germany was founded in the year 1543.

Source: Prime Curios!

639

639 = 3 x 3 x 71.

639 is the sum of the first 20 primes.

639 is the smallest number that is the sum of the first several primes and is congruent with 3 modulo 4.

639 is a number n whose fifth root has a decimal part that begins with n.

639 has the representation 639 = 3⁶ - 90.

Source: Number Gossip

9866

9866 = 2 x 4933.

9866 has a representation as a sum of two squares: 9866 = 29² + 95².

9866 is the number of words of length 45 in a certain language (A005819).

9866 is the sum of the proper divisors of the number of partitions of 34 (A139055).

9866 is the number of 6 x 6 arrays of squares of integers, symmetric about both diagonal and antidiagonal with all rows summing to 26 (A156389 and A156485).

Source: On-Line Encyclopedia of Integer Sequences

1473

1473 = 3 x 491.

1473 is an odd number whose sum of prime factors is palindromic (A046353): 3 + 491 = 494.

1473 is a semiprime (A001358) that is the sum of a semiprime k and the kth semiprime (A100467).

1473 is the number of lattice points inside the right triangle with legs 16 x 3 and 16 x 4 (and hypotenuse 16 x 5) (A126587).

1473 is the sum of the digit reversals of the first 41 natural numbers (A062918).

1473 is the smallest number that can be expressed as the sum of distinct Lucas numbers (A000204) in exactly 27 ways (A055635).

The leftmost digit of 1473 gives the number of even digits in 1473 and the rightmost digit of 1473 gives the number of odd digits in the number (A107837).

Mathematician and astronomer Nicolaus Copernicus was born in the year 1473.

Source: On-Line Encyclopedia of Integer Sequences