## Tuesday, July 31, 2012

### 121

121 = 11 x 11.

121 is the smallest multidigit palindromic square. It is also the smallest palindromic composite such that some permutation of digits is prime. It is the only odd palindromic square with an odd number of digits that is divisible by a palindromic prime number with an even number of digits.

121 is a perfect square. It is also a centered octagonal number and a centered dodecagonal number.

Every number greater than 121 is the sum of distinct primes of the form 4n + 1.

121 is 11111 in base 3.

121 is the maximum number of regions into which 15 lines divide a plane.

121 can be expressed as the sum of a prime and its reversal for exactly three distinct primes: 121 = 29 + 92 = 47 + 74 = 83 + 38.

121 = 1 + 31 + 32 + 33 + 34.

121 is the number of points required to win a standard game of cribbage.

Source: Prime Curios!

## Monday, July 30, 2012

### 802

802 = 2 x 401.

802 is the number of ways to toss a coin 10 times and not get a run of five (A135492).

802 has a representation as a sum of two squares: 802 = 192 + 212.

802 is 414 in base 14.

802 is the sum of eight consecutive primes (A127335): 802 = 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113.

8022 is the sum of two consecutive primes (A074924): 8022 = 643204 = 321593 + 321611.

802 is the number of isomers of the hydrocarbon chemical compound C13H28.

Source: On-Line Encyclopedia of Integer Sequences

## Friday, July 27, 2012

### 401

401 is a prime number.

401 is the start of the first occurrence of three consecutive primes using no prime digits: 401, 409, 419.

401 is the sum of seven consecutive primes: 401 = 43 + 47 + 53 + 59 + 61 + 67 + 71. It is also the sum of nine consecutive primes: 401 = 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61.

401 is a divisor of 204 - 1.

401 has a representation as a sum of two squares: 401 = 12 + 202.

401 is the hypotenuse of a primitive Pythagorean triple: 4012 = 402 + 3992.

401 was the hull number of the RMS Titanic.

Source: Number Gossip

## Thursday, July 26, 2012

### 783

783 = 3 x 3 x 3 x 29.

783 is a heptagonal number.

783 is the number of 11-ominoes that tile the plane by translation.

7833 = 480,048,687 = (48 + 00 + 48 + 687)3.

783 is 373 in base 15 and 234 in base 19.

## Wednesday, July 25, 2012

### 679

679 = 7 x 97.

679 is the smallest number with multiplicative persistence 5 (A003001 and A064869).

679 is the sum of three consecutive primes: 679 = 223 + 227 + 229 (A034961). It is also the sum of nine consecutive primes (A127336): 679 = 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97.

679 is the sum of nine positive fifth powers (A003354): 679 = 35 + 35 + 25 + 25 + 25 + 25 + 25 + 25 + 15.

The sum of the digits of 679 (6 + 7 + 9 = 22) exceeds the sum of the digits of 6792 (4 + 6 + 1 + 0 + 4 + 1 = 17) (A064399).

Source: Number Gossip

## Tuesday, July 24, 2012

### 494

494 = 2 x 13 x 19.

494 has the representation 494 = 29 - 18.

The product of the first 494 composite numbers minus 1 is prime.

494 + 209 = 703 and 494,207 = 7032.

494 is 3434 in base 5.

Source: Prime Curios!

## Monday, July 23, 2012

### 868

868 = 2 x 2 x 7 x 31.

4868 - 3 is a prime number.

868 has a square root whose decimal part starts with the digits 1 to 9 in some order: 29.461839725. . .

868 is 4004 in base 6 (A029963).

868 is the number of ways of writing 60 as a sum of eight nonnegative cubes (A173681).

Source: Prime Curios!

## Friday, July 20, 2012

### 396

396 = 2 x 2 x 3 x 3 x 11.

396 is a nonagonal number.

396 is the number of positions in a 3 x 3 sliding puzzle that require exactly 11 moves to solve starting with the hole in a corner.

396 is 112200 in base 3 and 1500 in base 6.

396 is the sum of a twin prime pair: 396 = 197 + 199.

396 refers to the displacement in cubic inches of early Chevrolet Big-Block engines.

## Thursday, July 19, 2012

### 296

296 = 2 x 2 x 2 x 37.

296 is the number of integer partitions of 30 into distinct parts.

296 has a representation as a sum of two squares: 296 = 102 + 142.

296 x 333,667 = 98,765,432.

296 is 1212 in base 6.

## Wednesday, July 18, 2012

### 252

252 = 2 x 2 x 3 x 3 x 7.

252 is the smallest number that is the product of two distinct numbers that are reverse of each other: 252 = 12 x 21.

252 = 28 - 4.

252 is the third value of Ramanujan's tau function (A000594).

252 is a hexagonal pyramidal number.

If you flip a coin 10 times in a row, there are exactly 252 ways in which it can turn out that you get exactly five heads and five tails.

Source: Number Gossip

## Tuesday, July 17, 2012

### 574

574 = 2 x 7 x 41.

574 is the maximum number of pieces into which a torus can be cut by 14 slices.

574 is 210021 in base 3. It is 707 in base 9.

574 is the number of sevens among the digits of all four-digit primes (A152279).

5742 = 329476 contains exactly six different digits (A054034).

## Monday, July 16, 2012

### 759

759 = 3 x 11 x 23. It is the product of three distinct Sophie Germain primes (A157346).

759 is 1001010 in base 3. It is 3303 in base 6 and 1033 in base 9 (and 2133 in base 7 and 533 in base 12).

759 is the sum of five consecutive primes (A034964): 759 = 139 + 149 + 151 + 157 + 163.

759 is a triangular matchstick number (A045943).

759 is the number of sets of natural numbers less than 37 that sum to 37 (A111133).

Source: On-Line Encyclopedia of Integer Sequences

## Friday, July 13, 2012

### 662

662 = 2 x 331.

662 is a divisor of 313 - 1.

662 is the index of the smallest triangular number that contains the digits 1, 2, 3, 4, and 5 (219,453).

662 is 220112 in base 3 and 22112 in base 4. It is 10122 in base 5 and 3022 in base 6.

662 is the sum of 12 consecutive primes (A127339): 662 = 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79.

## Thursday, July 12, 2012

### 753

753 = 3 x 251.

753 is a divisor of 2010 - 1.

753 is the smallest composite number that you can get by concatenating all odd primes up to some number in decreasing order.

753 is the smallest number whose cube contains four consecutive sevens: 7533 = 426957777.

753 is 353 in base 15.

Source: Number Gossip

## Wednesday, July 11, 2012

### 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

## Tuesday, July 10, 2012

### 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!

## Monday, July 9, 2012

### 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!

## Friday, July 6, 2012

### 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!

## Thursday, July 5, 2012

### 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).

## Tuesday, July 3, 2012

### 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.

## Monday, July 2, 2012

### 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!