## Friday, September 28, 2012

### 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!

## Thursday, September 27, 2012

### 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!

## Wednesday, September 26, 2012

### 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

## Tuesday, September 25, 2012

### 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

## Monday, September 24, 2012

### 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).

## Friday, September 21, 2012

### 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

## Thursday, September 20, 2012

### 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

## Wednesday, September 19, 2012

### 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

## Tuesday, September 18, 2012

### 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!

## Monday, September 17, 2012

### 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!

## Friday, September 14, 2012

### 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.

## Thursday, September 13, 2012

### 649

649 = 11 x 59.

649 is a semiprime whose digits are each a semiprime (A107342).

649 is the smallest number n so that n2 is 1 more than 13 times a square: 6492 = 1 + 13(180)2.

649 is 345 in base 14.

649 is a brilliant number (A078972).

Gliese 649 is a red dwarf star in the constellation of Hercules.

## Wednesday, September 12, 2012

### 552

552 = 2 x 2 x 2 x 3 x 23.

552 is an oblong or pronic number (of the form n(n + 1)) (A002378): 552 = 23 x 24.

552 is the number of prime knots with 11 crossings (A002863).

552 is the sum of six consecutive primes: 552 = 79 + 83 + 89 + 97 + 101 + 103. It is also the sum of 10 consecutive primes: 552 = 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73.

552 is the sum of six positive fifth powers (A003351): 552 = 35 + 35 + 25 + 25 + 15 + 15.

The German submarine U-552, nicknamed "Red Devil," was in service during World War II.

## Tuesday, September 11, 2012

### 338

338 = 2 x 13 x 13.

338 is the last integer for which the number of divisors (6) and the sum of its prime factors (2 + 13 + 13 = 28) are both perfect numbers.

338 is 2323 in base 5 and 242 in base 12.

338 has two representations as a sum of two squares: 338 = 72 + 172 = 132 + 132.

338 is a divisor of 994 - 1.

3383 = 38,614,472 = (386 + 1 - 4 - 47 + 2)3.

Source: Prime Curios!

## Monday, September 10, 2012

### 620

620 = 2 x 2 x 5 x 31.

620 is the number of one-sided 7-hexes (or hexagonal polyominoes with 7 cells) (A006535).

620 is the sum of four consecutive primes (A034963): 620 = 149 + 151 + 157 + 163. It is also the sum of eight consecutive primes (A127335): 620 = 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97.

The sum of the first 620 primes is a prime number (A013916).

620 is the sum of twelve positive fifth powers (A003357): 620 = 35 + 35 + 25 + 25 + 25 + 25 + 15 + 15 + 15 + 15 + 15 + 15.

## Friday, September 7, 2012

### 216

216 = 2 x 2 x 2 x 3 x 3 x 3.

216 = 63 is a perfect cube. 216 = 6(2 + 1).

216 = 21 + 20 + 19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6.

216 is the smallest cube that can be written as the sum of three cubes: 216 = 53 + 43 + 33.

216 is the smallest number that can be expressed as the difference of the sums of the squares of successive twin primes: 216 = (132 + 112) - (72 + 52).

216 is 1331 in base 5.

216 is the sum of a twin prime pair: 216 = 107 + 109.

In the film Pi, Max Cohen becomes obsessed with a 216-digit number in his quest to find a numeric equation behind existence.

Source: Prime Curios! and Wikipedia

## Thursday, September 6, 2012

### 539

539 = 7 x 7 x 11.

539 is the number of multigraphs with five vertices and nine edges.

539 is 2255 in base 6 and 1400 in base 7.

539 is the sum of two distinct positive cubes (A024670): 539 = 83 + 33.

Inserting the digit 9 between adjacent digits of 539 makes a prime (A050719): 59399.

539 is the sum of 11 consecutive primes (A127338): 539 = 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71.

## Wednesday, September 5, 2012

### 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.

## Tuesday, September 4, 2012

### 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!