## Friday, June 28, 2013

### 887

887 is a prime number.

887 is the smallest prime p such that the next consecutive prime is p + 20 (907) (A000230 and A031938).

887 is a prime that results from merging three consecutive digits in the decimal expansion of the golden ratio (A103811). It also results from merging three successive digits in the decimal expansion of the square root of 2 (A198163).

887 is a prime that remains a prime when a single zero is inserted between any two adjacent digits (A215417): 8087 and 8807 are primes.

887 is 1101110111 in base 2 (binary). It is 31313 in base 4.

In 1896, Yorkshire hit up a still-standing County Championship cricket record total of 887 runs against Warwickshire.

Source: Prime Curios!

## Thursday, June 27, 2013

### 1459

1459 is a prime number.

1459 is the only four-digit number with the following property: the sum of the first and second digits is the third digit, the sum of the second and third digits is the fourth digit, and the sum of the third and fourth digits is the first two digits.

919 = 13 + 43 + 53 + 93 and 1459 = 93 + 13 + 93. This is the smallest pair of prime numbers that are mutually the sum of the same powers of each others digits. Equivalently, 1459 is the sum of the cubes of the digits of the sum of the cubes of its digits.

1459 is the smallest prime made up of all the distinct digits in which squares of primes end.

1459 = 11 + 444 + 5 + 999.

1459 is a divisor of 599 - 1.

1459 is 2000001 in base 3.

Source: Prime Curios!

## Wednesday, June 26, 2013

### 9462

9462 = 2 x 3 x 19 x 83.

9462 is 22366 in base 8.

9462 is a number n such that the sum of the cubes of the digits of n3 is a perfect cube (A164882).

9462 is a number n such that n2 ends in the digits 444 (A039685).

9462 is the average of a twin-prime pair for a pair in which each prime is expressible as the sum of two triangular numbers (A117313).

9462 is the number of asymmetric (identity) trees with 41 nodes and four leaves (A055335).

Source: On-Line Encyclopedia of Integer Sequences

## Tuesday, June 25, 2013

### 678

678 = 2 x 3 x 113. It is the product of three distinct Sophie Germain primes (A157346).

678 is a member of the Fibonacci-like sequence starting with 1 and 7 (A022097).

The sum of the squares of the first 678 primes is a prime (A098561).

678 is the sum of eight positive fifth powers (A003353): 678 = 35 + 35 + 25 + 25 + 25 + 25 + 25 + 25.

678 and the 678th prime (5077) have only the digit 7 in common (A107938).

## Monday, June 24, 2013

### 478

478 = 2 x 239.

478 is the seventh Pell-Lucas number (A002203).

478 is the number of primes less than 3,400 (A028505).

478 is the number of ways of making change for 53 cents using coins of 1, 2, 5, 10, 25, and 50 cents (A001302).

478 is 111011110 in base 2 (binary).

## Friday, June 21, 2013

### 326

326 = 2 x 163.

326 is the maximum number of regions into which 25 lines divide a plane (A000124).

326 is the number of permutations of some subset of five elements (A000522).

326 is the sum of 14 consecutive primes: 326 = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47.

326 is a number n such that n and n + 1 (327) are semiprimes (A070552) and have the same number of divisors (A005237).

The sum of the first 326 primes is a prime (A013916).

## Thursday, June 20, 2013

### 5209

5209 is a prime number.

5209 is the largest minimal prime in base 6 (40041).

The reversal of 5209 is a square (9025 = 952) (A007488).

5209 is the lower prime of a difference of 18 between consecutive primes (A031936). It is also the first of two consecutive primes with equal digital sums (A066540): 5 + 2 + 0 + 9 = 16 and 5 + 2 + 2 + 7 = 16.

5209 has a representation as a sum of two squares: 5209 = 52 + 722.

5209 is the hypotenuse of a primitive Pythagorean triple: 52092 = 7202 + 51592.

5209 is a divisor of 3514 - 1.

Source: Prime Curios!

## Wednesday, June 19, 2013

### 577

577 is a prime number.

577 is one of only two prime numbers with a square of the form AABCBC: 5772 = 332929.

577 is the larger of only two three-digit primes that remain prime when inserting one, two, or three zeroes between each digit: 50707, 5007007, 500070007 are primes. The other such prime is 131.

577 has a representation as a sum of two squares: 577 = 12 + 242.

577 is the hypotenuse of a primitive Pythagorean triple: 5772 = 482 + 5752.

577 is 1001000001 in base 2 (binary).

577 is a divisor of 244 - 1.

577 is the number of isomers of the C60H3 Buckminsterfullerene molecule.

Source: Prime Curios!

## Tuesday, June 18, 2013

### 463

463 is a prime number.

461 and 463 form a twin prime pair.

463 is a centered heptagonal number.

463 is the smallest multidigit prime such that both the sum of the digits and the product of the digits of its square remain square.

463 divided by 595 is an excellent approximation to the common logarithm of 6.

463 is 111001111 in base 2 (binary).

463 is a divisor of 213 - 1.

463 meters is exactly one-fourth of an international nautical mile.

Source: Prime Curios!

## Monday, June 17, 2013

### 994

994 = 2 x 7 x 71.

994 is the maximum number of regions into which 32 circles divide the plane.

994 is the smallest number with the property that its first 18 multiples contain the digit 9.

994 = 497 x 2 and, in reverse, 499 = 497 + 2.

994 is a sum of positive powers of its digits (A007532): 994 = 93 + 91 + 44.

## Friday, June 14, 2013

### 530

530 = 2 x 5 x 53.

530 is the sum of the first three perfect numbers: 530 = 6 + 28 + 496.

530 is 1000010010 in base 2 (binary).

530 has two representations as a sum of two squares: 530 = 12 + 232 = 132 + 192.

530 is a divisor of 234 - 1.

Halley's Comet was visible from Earth in the year 530.

## Thursday, June 13, 2013

### 4720

4720 = 2 x 2 x 2 x 2 x 5 x 59.

4720 is a structured truncated cubic number (A100152).

4720 is an octagonal (star) number (A000567). The product of its digits is also an octagonal number (A117083): 4 x 7 x 2 x 0 = 0.

4720 is a number such that 4720 and 47202 = 22278400 use only the digits 0, 2, 4, 7, and 8 (A136906).

## Wednesday, June 12, 2013

### 492

492 = 2 x 2 x 3 x 41.

492 has the representation 492 = 29 - 20.

492 is a hexanacci number.

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

492 is the sum of six consecutive primes: 492 = 71 + 73 + 79 + 83 + 89 + 97. It is also the sum of two successive primes (A001043): 492 = 241 + 251.

492 is a refactorable number; the number of divisors of 492 divides 492 (A033950).

## Tuesday, June 11, 2013

### 2400

2400 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5.

2400 is 6666 in base 7.

2400 is a number that can be expressed as the difference of the squares of primes in just two distinct ways (A090788).

2400 is the total number triangles visible in a regular decagon with all diagonals drawn (A006600).

2400 is the number of ways of writing 11 as a sum of six squares (A000141).

2400 is the difference of two fourth powers (A147857).

## Monday, June 10, 2013

### 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

## Friday, June 7, 2013

### 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!

## Thursday, June 6, 2013

### 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).

## Wednesday, June 5, 2013

### 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).

## Tuesday, June 4, 2013

### 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

## Monday, June 3, 2013

### 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).