## Monday, April 30, 2012

### 188

188 = 2 x 2 x 47.

188 is the number of connected bipartite graphs with eight vertices.

188 is the largest known even number that can be expressed as the sum of two distinct primes in exactly five ways.

188 is the number of semigroups of order 4.

1883 = 6,644,672 = (6 + 64 + 46 + 72)3.

188 = 22 + 32 + 72 + 112.

188 Menippe is an asteroid discovered in 1878.

Source: Prime Curios!

## Friday, April 27, 2012

### 291

291 = 3 x 97.

291 is the smallest semiprime with prime factors adding up to 100.

291 is the largest number that is not the sum of distinct non-trivial powers.

291 is 2131 in base 5. It is 10203 in base 4 and 1203 in base 6. It is 353 in base 9 (A029955) and 123 in base 16 (A048447).

Inserting a digit '1' between adjacent digits of 291 makes a prime (A050711): 21911 is prime.

291 was an arts and literary magazine published from 1915 to 1916 in New York City.

Source: Number Gossip

## Thursday, April 26, 2012

### 1267

1267 = 7 x 181.

1267 is 5511 in base 6. It ends with the digit 7 in bases 9, 10, 12, 14, 15, 18, 20, 21, 28, and 30.

1267 is the sum of two positive fifth powers (A003347): 1267 = 45 + 35.

1267 is the sum of nine consecutive primes (A127336): 1267 = 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 + 163.

12672 = 1605289 contains exactly seven different digits (A054035).

1267 is the maximum number of points visible from some point in a square 45 x 45 lattice (A141224).

Source: On-Line Encyclopedia of Integer Sequences

## Wednesday, April 25, 2012

### 629

629 = 17 x 37.

629 is a brilliant number (A078972). It is a semiprime whose prime factors have the same number of decimal digits.

629 is a powerful number (A007532). It can be written as a sum of positive powers of its digits: 629 = 62 + 29 + 92.

629 is 2525 in base 6. It is 275 in base 16 and 125 in base 24.

629 has two representations as a sum of two squares: 629 = 22 + 252 = 102 + 232.

629 is the hypotenuse of two primitive Pythagorean triples: 6292 = 1002 + 6212 = 4292 + 4602.

Source: On-Line Encyclopedia of Integer Sequences

## Tuesday, April 24, 2012

### 828

828 = 2 x 2 x 3 x 3 x 23.

There are 828 primes between 180,000 and 190,000 (A038824).

There are 828 ways to write 42 as the sum of nine nonnegative cubes (A173682).

828 is the sum of nine positive fifth powers (A003354): 828 = 35 + 35 + 35 + 25 + 25 + 25 + 15 + 15 + 15.

828 is a number with 18 divisors (A030636).

The sum of the base 3 digits of 828 (1010200) equals the sum of the base 9 digits of 828 (1120) (A037314).

Source: On-Line Encyclopedia of Integer Sequence

## Monday, April 23, 2012

### 1159

1159 = 19 x 61.

1159 is a centered octahedral number (A001845).

1159 is a member of the Mian-Chowla sequence (A005282).

1159 is the sum of the first 39 nonprimes (A051349).

1159 is the maximum number of points visible from some point in a square 43 x 43 lattice (A141224).

## Friday, April 20, 2012

### 408

408 = 2 x 2 x 2 x 3 x 17.

408 is the sum of four consecutive primes: 408 = 97 + 101 + 103 + 107. It is also the sum of eight consecutive primes: 408 = 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67.

408 is an octagonal number.

408 is the eighth Pell number.

408 is 3113 in base 5, 1122 in base 7, and 212 in base 14.

408 is the telephone area code for the Silicon Valley, California.

## Thursday, April 19, 2012

### 330

330 = 2 x 3 x 5 x 11.

330 is the eighth pentatope number. It is also a pentagonal number.

3303 + 3303 + 3300 is a prime number.

330 is the sum of six consecutive primes: 330 = 43 + 47 + 53 + 59 + 61 + 67.

330 is the sum of five consecutive squares: 330 = 62 + 72 + 82 + 92 + 102.

Source: Prime Curios!

## Wednesday, April 18, 2012

### 6081

6081 = 3 x 2027.

6081 has a cube that is the sum of three positive cubes.

6081 is 4629 in base 11 and 3629 in base 12.

6081 is a concentric 16-gonal number (A195146). It is also a centered 32-gonal number (A195315).

6081 is the sum of the first 54 primes (A109722).

## Tuesday, April 17, 2012

### 615

615 = 3 x 5 x 41. It is the product of three distinct Sophie Germain primes (A157346).

615 is a hypotenuse for which there exist four distinct integer triangles (A084648).

615 is the sum of seven positive fifth powers (A003352): 615 = 35 + 35 + 25 + 25 + 25 + 25 + 15.

The sum of the even digits of 615 equals the sum of the odd digits of 615 (A036301).

Source: On-Line Encyclopedia of Integer Sequences

## Monday, April 16, 2012

### 527

527 = 17 x 31.

527 is the smallest number n for which there do not exist four smaller numbers so that a1! a2! a3! a4! n! is square.

527 is 252 in base 15.

527 is a brilliant number (A078972). It is a semiprime whose prime factors have the same number of digits.

Section 527 of the U.S. Tax Code regulates soft money political campaigning.

## Friday, April 13, 2012

### 603

603 = 3 x 3 x 67.

The first 603 digits of 603603 form a 2002-bit prime.

603 is the smallest number n so that n, n + 1, and n + 2 are all the product of a prime and the square of a prime: 603 = 67 x 32; 604 = 151 x 22; 605 = 5 x 112.

6032 = 363609 = (3 - 6 - 3 + 609)2.

603 is 1133 in base 8, 311 in base 14, and 113 in base 24.

Source: Prime Curios!

## Thursday, April 12, 2012

### 1425

1425 = 3 x 5 x 5 x 19.

1425 is 10110010001 in base 2 (binary). It is a self-descriptive number in base 5: 21200.

The sum of the digits of 1425 is equal to the number of divisors of 1425 (1, 3, 5, 15, 19, 25, 57, 75, 95, 285, 475, 1425): 1 + 4 + 2 + 5 = 12 (A057531 and A057532).

1425 is the sum of the first 31 semiprimes (A062198).

Every digit occurs at least once in 14254: 4,123,437,890,625 (A121321).

Source: On-Line Encyclopedia of Integer Sequences

## Wednesday, April 11, 2012

### 4646

4646 = 2 x 23 x 101.

The digits of 4646 are all semiprimes (A111494 and A107665).

54646 - 46465 is a prime (A117705).

4646 and the 4646th prime (44699) contain only the digits 4, 6, and 9 (A107624).

4646 is the number of connected graphs on eight nodes with clique number 4 (A126746).

Source: On-Line Encyclopedia of Integer Sequences

## Tuesday, April 10, 2012

### 485

485 = 5 x 97.

485 has two representations as a sum to two squares: 485 = 12 + 222 = 142 + 172.

485 is the hypotenuse of two primitive Pythagorean triples: 4852 = 442 + 4832 = 932 + 4762.

485 is the number of categories with six morphisms and two objects.

485 is 345 in base 12. It is 101 in base 22.

## Monday, April 9, 2012

### 238

238 = 2 x 7 x 17.

238 is the sum of the first 13 primes: 238 = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41.

238 is the number of connected partial orders on six unlabeled elements.

238 is 11101110 in base 2 (binary). It is 3232 in base 4.

238 is a tridecagonal number (A051865).

U-238 is the non-fissile isotope of uranium that is the heaviest isotope of any material available through extraction from minerals.

## Friday, April 6, 2012

### 660

660 = 2 x 2 x 3 x 5 x 11.

660 is 1010010100 in base 2 (binary). It is 220110 in base 3 and 22110 in base 4.

660 is the order of a non-cyclic simple group.

660 is the sum of four consecutive primes: 660 = 157 + 163 + 167 + 173. It is also the sum of six consecutive primes: 660 = 101 + 103 + 107 + 109 + 113 + 127. And the sum of eight consecutive primes: 660 = 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101.

660 is the number of feet in a furlong.

## Thursday, April 5, 2012

### 3518

3518 = 2 x 1759.

3518 is 24142 in base 6. It is the 40th base-6 palindrome that starts with 2 (A043011).

3518 is the smallest of four consecutive integers divisible by four consecutive primes (A072555): 3518 = 2 x 1759; 3519 = 3 x 3 x 17 x 23; 3520 = 2^6 x 5 x 11; 3521 = 7 x 503.

The constants pi, e, and phi have the same decimal digit in the 3518th place (A090230).

Source: Positive Integers

## Wednesday, April 4, 2012

### 373

373 is a prime number.

373 is the only palindromic prime with all substrings prime. It is the largest prime such that each substring is prime.

373 is the sum of the squares of five consecutive primes: 373 = 32 + 52 + 72 + 112 + 132.

373 = 21 + 31 + 52 + 73 is the sum of the first four primes raised to the powers of the first four Fibonacci numbers.

373 has a representation as a sum of two squares: 373 = 72 + 182.

373 is the hypotenuse of a primitive Pythagorean triple: 3732 = 2522 + 2752.

Water boils at a temperature under standard conditions of about 373 kelvins.

Source: Prime Curios!

## Tuesday, April 3, 2012

### 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

## Monday, April 2, 2012

### 646

646 = 2 x 17 x 19.

646 is a divisor of 696 - 1.

646 is the number of connected planar graphs with 7 vertices (A003094).

646 is 787 in base 9.

646 is the sum of seven positive fifth powers: 646 = 35 + 35 + 25 + 25 + 25 + 25 + 25.