5356

5356 = 2 x 2 x 13 x 103.

5356 is the 103rd triangular number. It is also a centered nonagonal number (A060544). It is a triangular number whose digit reversal is a semiprime (A115742). It is also a triangular number for which the sum of digits is a prime number (A117512).

5356 is the number of inequivalent ways to place a pair of checkers on a 17 x 17 board (A014409).

5356 is the number of complete squares that fit inside a circle with radius 42, drawn on squared paper (A119677).

5356 divides 47¹² - 1.

5356 is 40444 in base 6 (A043388). It is 12354 in base 8.

Source: OEIS

8128

8128 = 2 x 2 x 2 x 2 x 2 x 2 x 127.

8128 is a perfect number (2^{7 - 1}(2⁷ - 1)), associated with the Mersenne prime 127 = 2⁷ - 1 (A000396). It is the largest perfect number whose index (4) is equal to the number of digits.

8128 is the 127th triangular number; it is the sum of the first 127 integers. 8128 is the 64th hexagonal number. It is also a centered nonagonal number (A060544).

8128 divides 63¹⁴ - 1.

Source: Number Gossip

1081

1081 = 23 x 47.

1081 is the 46th triangular number (the sum of the first 46 integers) (A000217 and A068443). It is also a centered nonagonal number (A060544).

1081 is a member of the Padovan sequence (A000931).

1081 is a concentric dodecagonal number (A195143).

1081 is the sum of 11 consecutive primes (A127338).

1081 is the smallest semiprime and brilliant number that is prime when reversed and turned upside down.

1081 divides 93² - 1.

Source: Prime Curios!

666

666 = 2 x 3 x 3 x 37.

666 is the 36th triangular number; it is the sum of the first 36 positive integers. It is the largest triangular number that consists of the same repeated digit.

666 is the sum of the squares of two consecutive triangular numbers: 666 = (15 x 15) + (21 x 21).

666 is the sum of two consecutive palindromic primes: 666 = 313 + 353.

666 is the sum of the squares of the first seven prime numbers: 666 = 2² + 3² + 5² + 7² + 11² + 13² + 17².

666 has a representation as a sum of two squares: 666 = 15² + 21².

There are exactly 666 twin primes less than 6⁶ + 666.

666 has the representation 3⁶ - 63.

666 lists in their proper order the letters used for numbers in the Roman numeration system: D (500) + C (100) + L (50) + X (10) + V (5) + I (1), or DCLXVI.

666 is the sum of all the numbers on a typical roulette wheel.

Source: Prime Curios!

2628

2628 = 2 x 2 x 3 x 3 x 73.

2628 is the 72nd triangular number (the sum of the first 72 positive integers). Note that its external digits, 2 and 8, form a triangular number when concatenated (A077367). It is the least triangular number divisible by the 21st prime (A112456).

2628 is 101001000100 in base 2 (binary). 2628 contains only the digits 0, 1, and 2 in bases 3, 4, and 6.

2628 is a divisor of 65⁶ - 1.

2628 has a representation as a sum of two squares (A073613): 2628 = 18² + 48².

Source: On-Line Encyclopedia of Integer Sequences

595

595 = 5 x 7 x 17.

595 is the 34th triangular number (the sum of the first 34 integers).

595 is a centered nonagonal number.

595 is the number of ways to tile a 3 x 18 rectangle with 3 x 1 rectangles.

595 is 151 in base 22.

Source: Whar's Special About This Number?

561

561 = 3 x 11 x 17.

561 is 1000110001 in base 2 (binary) (A006995).

561 is the 33rd triangular number (A000217), the sum of the first 33 integers. It is also a hexagonal number (A000384) and a dodecagonal number (A051624).

561 is the smallest Carmichael number (A002997).

561 is a centered icosahedral number (cuboctahedral number) (A005902).

Source: Number Gossip

4656

4656 = 2 x 2 x 2 x 2 x 3 x 97.

4656 is the 96th triangular number, with digit sum 21 (A068131).

4656 is 1020300 in base 4 and 1230 in base 16.

4656 is a structured pentagonal hexacontahedral number (A100169).

4656 is the number of 3 x 3 arrays of squares on integers summing to 18 (A159401).

Source: Numeropedia

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!

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!

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

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

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

741

741 = 3 x 13 x 19.

741 is the 13th triangular number (A000217).

741 is a divisor of 77² - 1.

741 is not expressible as the sum of a prime and a triangular number (A076768).

741 and 742 have three distinct prime factors (A140077).

Source: On-Line Encyclopedia of Integer Sequences

153

153 = 3² x 17.

153 is the 17th triangular number. It is also a hexagonal number.

153 = 1! + 2! + 3! + 4! + 5!

153 is palindromic in base 2 (binary): 10011001. It is 2121 in base 4 and 99 in base 16.

153 is the smallest number greater than 1 such that the sum of the cubes of its digits equals itself: 153 = 1³ + 5³ + 3³.

153 has a representation as a sum of two squares: 153 = 3² + 12².

In the Bible, Simon Peter is said to have caught 153 fish (John 21:11).

Source: Number Gossip

378

378 = 2 x 3³ x 7.

378 is the 27th triangular number. It is also a hexagonal number and the smallest Smith triangular number.

378 is the smallest three-digit number in which the sum of the digits is equal to the sum of the prime factors: 3 + 7 + 8 = 2 + 3 + 3 + 3 + 7 = 18.

378 is a cake number.

378 Holmia is an asteroid discovered in 1893.

Source: Number Gossip

276

276 = 2² x 3 x 23.

276 is the 23rd triangular number.

276 is the magic sum of a magic square made up of 16 consecutive primes.

276 is the largest difference between two consecutive primes less than 10⁹.

276 = 1⁵ + 2⁵ + 3⁵.

Loctite 276 is an adhesive for the permanent locking and sealing of threaded fasteners.

Source: Prime Curios!

861

861 = 3 x 7 x 41.

861 is the 41st triangular number. It is also a hexagonal number.

861 = 7 + 77 + 777.

144,648 = 861 x 168 = 492 x 294.

The USS Harwood (DD 861) was a destroyer in the U.S. Navy just after World War II.

Source: What's Special About This Number?

351

351 = 3³ x 13.

351 is the 26th triangular number. It is the sum of the first 26 numbers. Hence, it is also the numeric value of all the letters of the English alphabet, taken together.

351 is a number that cannot be written as a sum of three squares.

351 is a divisor of 53² - 1.

351 is the smallest number so that it and its immediate neighbors are each the product of four or more primes: 350 = 2 x 5 x 5 x 7; 351 = 3 x 3 x 3 x 13; 352 = 2 x 2 x 2 x 2 x 2 x 11.

The 1971 Ford Mustang Boss 351 was equipped with a powerful 351-cubic-inch V-8 engine.

Source: Number Gossip