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?