## Friday, August 30, 2013

### 3407

3407 is a prime number.

3407 is 11200012 in base 3, 102112 in base 5, and 1022 in base 15.

3407 is a prime that is the sum of four consecutive composite numbers (A060329): 3407 = 850 + 851 + 852 + 854.

3407 is the upper prime of a difference of 16 between consecutive primes (A031935).

3407 is a number n such that googol - n is a prime (A108251).

Source: On-Line Encyclopedia of Integer Sequences

## Thursday, August 29, 2013

### 1560

1560 = 2 x 2 x 2 x 3 x 5 x 13.

1560 is a pronic number because it is the product of two consecutive integers (A002378): 1560 = 39 x 40.

1560 is 11000011000 in base 2 (binary). It can be expressed using only the digits 0, 1, and 2 in bases 2, 3, 4, 5, and 6. It is 3030 in base 8.

1560 is the maximum number of pieces into which a torus can be sliced using 20 cuts.

1560 is a number n such that 11n + 1 (A219257) and 21n + 1 (A219391) are squares: 11(1560) + 1 = 17161 = 1312 and 21(1560) + 1 = 32761 = 1812.

1560 is the number of ways, counted up to symmetry, to build a contiguous structure with 3 LEGO blocks of size 2 x 4 (A112389).

Source: Number Gossip

## Wednesday, August 28, 2013

### 3221

3221 is a prime number.

3221 has a representation as a sum of two squares: 3221 = 142 + 552.

3221 is the hypotenuse of a primitive Pythagorean triple: 32212 = 15402 + 28292.

3221 is a divisor of 115 - 1.

3221 is the sum of four positive fifth powers (A003349): 3221 = 55 + 25 + 25 + 25.

3221 is a number n such that googol - n is prime (A108251).

Source: On-Line Encyclopedia of Integer Sequences

## Tuesday, August 27, 2013

### 1486

1486 = 2 x 743.

1486 is the number of different score sequences of a 10-team round-robin tournament (A000571).

1486 is 2001001 in base 3.

1486 is an even central polygonal number (A193868).

1486 is the number of labeled forests of 6 nodes, each component of which is a path (A011800).

1486 is the least value of k such that the decimal expansion of 18k contains seven consecutive identical digits (A217162).

## Monday, August 26, 2013

### 1411

1411 = 17 x 83.

1411 is the number of quasigroups of order 5 (A057991).

1411 is a composite number such that every concatenation of its prime factors (1783 and 8317) is prime (A217263).

1411 is a number n such that n3 is the sum of three successive primes (A076306).

1411 has the property that the sum of its divisors (excluding 1 and itself) is a square (A187086): 17 + 83 = 100 = 102.

1411 is the bar coding for 3 in the Universal Product Code (UPC).

Source: Number Gossip

## Friday, August 23, 2013

### 1297

1297 is a prime number.

1297 is 10100010001 in base 2 (binary) and 1210001 in base 3. Its base 2 and base 3 representations end with its base 6 representation: 10001.

1297 is the smallest four-digit prime that produces five other primes by changing only its first digit: 2297, 4297, 5297, 7297, and 8297.

1297 is the smallest prime whose reversal (7921) is the square of a Fibonacci number: 7921 = 892.

1297 has a representation as a sum of two squares: 1297 = 12 + 362. It has the representation 64 + 1.

1297 is a divisor of 364 - 1.

1297 is the hypotenuse of a primitive Pythagorean triple: 12972 = 722 + 12952.

Cartoon character Bugs Bunny once correctly calculated 1297 times 142 in his head and said, "If there's one thing we 'wabbits' can do, it's multiply."

Source: Prime Curios!

## Thursday, August 22, 2013

### 1012

1012 = 2 x 2 x 11 x 23.

1012 has a square that is formed by slightly rearranging its digits and inserting three 4s: 10122 = 1024144.

1012 is the sum of four consecutive primes (A034963): 1012 = 241 + 251 + 257 + 263.

1012 is the solution to the postage stamp problem for three denominations and 23 stamps (A001208).

1012 is the number of times the digit 4 appears in the first 104 digits of pi (A099295).

1012 is 4404 in base 6.

1012 has a unique representation as a sum of three squares: 1012 = 62 + 202 + 242.

1012 has the representation 210 - 12.

1012 is a divisor of 452 - 1.

## Wednesday, August 21, 2013

### 1914

1914 = 2 x 3 x 11 x 29. It is the product of four distinct primes (A046386).

1914 is the sum of 10 consecutive primes (A127337): 1914167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223.

1914 is the number of ways to dissect a nonsquare rectangle into 7 rectangles with equal area (A189243).

1914 is the number of prime pairs below 106 having a difference of 30 (A093750).

1914 is a number n such that the square of n (3,663,396) contains only the digits 3, 6, and 9 (A053948).

1914 was a year with exactly three "Friday the 13ths" (A190653).

Source: On-Line Encyclopedia of Integer Sequences

## Tuesday, August 20, 2013

### 1878

1878 = 2 x 3 x 313.

1878 is a number with three distinct palindromic factors (A046401).

1878 is 30003 in base 5.

1878 is the sum of two successive prime numbers (A206329): 1878 = 937 + 941. 18782 is also the sum of two successive prime numbers (A213739): 3526884 = 1763431 + 1763453.

1878 is the number of 2 x 2 integer matrices with elements from {1, . . ., 33} whose determinant is 2 (A197168).

1878 is a divisor of 254 - 1.

A transit of of the planet Mercury (as seen from Earth) occurred in the year 1878 (A171466).

Source: On-Line Encyclopedia of Integer Sequences

## Monday, August 19, 2013

### 785

785 = 5 x 157.

785 is 555 in base 12.

785 are the last three digits of the sum of the first 785 squares.

785 has two representations as a sum to two squares (A024508): 785 = 12 + 282 = 162 + 232.

785 is the hypotenuse of two primitive Pythagorean triples (A024409): 7852 = 562 + 7832 = 2732 + 7362.

785 is the sum of two distinct positive pentatope numbers (A104392).

785 is a number n such that every base 5 digit of n (11120) is a base 9 digit of n (1062) (A037396).

## Friday, August 16, 2013

### 1842

1842 = 2 x 3 x 307.

1842 is 11100110010 in base 2 (binary).

1842 is the number of rooted trees with 11 vertices (A000081).

1842 is 666 in base 17.

1842 is a number n such that p(n), p(n) + 6, p(n) + 12, and p(n) + 18 are consecutive primes, where p(n) denotes the nth prime (A090832): 15791, 15797, 15803, and 15809 are all primes.

1842 is the sum of eight nonzero 6th powers (A003364).

## Thursday, August 15, 2013

### 8110

8110 = 2 x 5 x 811.

8110 is the number of semiprimes less than 215 (A125527).

8110 has the property that the sum of its base 10 digits (10) is equal to the sum of its base 2 (binary digits) (A152207).

8110 has four 1s in its base 9 representation (A043460): 12111.

8110 is a number n with the property that the sum of the digits of n is a substring of n and of the square of n (A162015).

Source: On-Line Encyclopedia of Integer Sequences

## Wednesday, August 14, 2013

### 873

873 = 3 x 3 x 97.

873 = 1! + 2! + 3! + 4! + 5! + 6! (A007489).

873 is 1551 in base 8. It is 369 in base 16.

873 is the solution to the postage stamp problem for four denominations and 13 stamps (A001209).

873 is a number n such that 4n - 1, 8n - 1, and 16n - 1 are primes (A101790).

873 has a representation as a sum of two squares: 873 = 122 + 272.

873 is a divisor of 982 - 1.

## Tuesday, August 13, 2013

### 1802

1802 = 2 x 17 x 53.

1802 is the smallest number not ending in zero that can be represented as the sum of the squares of distinct primes in two different ways: 1802 = 112 + 412 = 292 + 312.

1802 is 2110202 in base 3, 24202 in base 5, and 12202 in base 6. It is 802 in base 15.

1802 is the sum of eight successive primes (A127335): 1802 = 199 + 211 + 223 + 227 + 229 + 233 + 239 + 241.

1802 is the number of 2 x 2 integer matrices with elements from {1, . . ., 32} whose determinant is 2 (A197168).

1802 is the maximum number of regions the plane is divided into by 25 triangles (A077588).

Source: Prime Curios!

## Monday, August 12, 2013

### 1775

1775 = 5 x 5 x 71.

1775 is 11011101111 in base 2 (binary). It has exactly nine 1s in its binary expansion (A023691).

1775 is a member of the Fibonacci-type sequence beginning with 1 and 7 (A022097).

1775 is the sum of all odd numbers in the range 350 to 359 (A053742).

1775 is the smaller of two consecutive numbers that are not the sum of three nonzero squares (A178615).

## Friday, August 9, 2013

### 3690

3690 = 2 x 3 x 3 x 5 x 41.

3690 is 12001200 in base 3 (A020331) and 5050 in base 9 (A020337).

3690 is the number of trees on 29 vertices with diameter 4 (A000094).

3690 is the number of 20-digit fifth powers (A216655).

3690 is a number n such that n and the square of n (13616100) use only the digits 0, 1, 3, 6, and 9 (A136850).

3690 has two representations as a sum of two squares: 3690 = 212 + 572 = 332 + 512.

3690 is a divisor of 734 - 1.

## Thursday, August 8, 2013

### 9763

9763 = 13 x 751.

9763 and its reversal 3679 are both multiples of 13 (A062912).

9763 is 113111 in base 6.

9763 is a number n such that 100n + 1, 100n + 3, 100n + 7, and 100n + 9 are all primes (A064687).

Southern Pacific 9763 is a diesel locomotive built in 1991.

Source: On-Line Encyclopedia of Integer Sequences

## Wednesday, August 7, 2013

### 1639

1639 = 11 x 149.

1639, 1641, and 1643 are semiprimes (A092125).

1639 is a nonagonal number (A001106).

1639 is the number of binary rooted trees with 16 vertices.

1639 is 2020201 in base 3 and 121213 in base 4. It is 2221 in base 9.

Every base 6 digit of 1639 is a base 10 digit of 1639: 11331 (A037401).

1639 is the sum of two pentagonal numbers in exactly two different ways (A064826).

## Tuesday, August 6, 2013

### 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!

## Monday, August 5, 2013

### 2215

2215 = 5 x 443.

2215 is the smallest product of two distinct odd primes greater than 472 (A099610).

2215 is a number whose product of digits is twice the sum of its digits (A062034).

2215 is 10001001 in base 3.

2215, 2216, 2217, 2218, and 2219 are all divisible by the same number of primes (A045933).

2215 is a year in which January 1 falls on a Sunday (A162244).

Source: On-Line Encyclopedia of Integer Sequences

## Friday, August 2, 2013

### 572

572 = 2 x 2 x 11 x 13.

572 is a number with exactly three prime digits (A092625).

572 is the smallest number that has equal numbers of every digit in base 2 (1000111100) and base 3 (210012) (A049354).

572 is 4242 in base 5. It is palindromic in base 3 (210012) (A014190) and base 15 (282).

572 is a number n such that n2 (327184) contains exactly six different digits (A054034).

572 x 574 = 328328 (A116286).

572 is a divisor of 214 - 1.

## Thursday, August 1, 2013

### 3402

3402 = 2 x 3 x 3 x 3 x 3 x 3 x 7.

3402 can be written as the sum of 2, 3, 4, or 5 positive cubes (A085338).

3402 is 102102 in base 5 (A020333).

3402 is the sum of the fifth powers of the first five Fibonacci numbers (A098531).

3402 is a number evenly divisible by twice the square of the sum of its digits (A085444).