## Friday, March 29, 2013

### 922

922 = 2 x 461.

922 is 1234 in base 9 (A048441).

The sum of 922 and its reversal is a prime: 922 + 229 = 1151.

922 is the middle number of three consecutive semiprimes (A086005): 921, 922, and 923.

922 is a Smith number (A006753).

922 has a representation as a sum of two squares: 922 = 92 + 292.

## Thursday, March 28, 2013

### 1588

1588 = 2 x 2 x 397.

1588 has a representation as a sum of two squares: 1588 = 122 + 382.

1588 is the sum of the totient function for the first 72 integers.

1588 is the maximum number of regions into which 4-space can be divided by 13 hyperspheres (A059173).

1588 is the sum of the path lengths of all binary trees with 5 edges (A138156).

The 1588th triangular number (1,261,666) contains only the digits 1, 2, and 6 (A119104).

Source: On-Line Encyclopedia of Integer Sequences

## Wednesday, March 27, 2013

### 376

376 = 2 x 2 x 2 x 47.

376 is a pentagonal number.

376 is an automorphic (or curious) number: 3762 = 141376, which ends with the digits 376. Indeed, all powers of 376 (or powers of any number ending in 376) end with 376.

There are 376 Smith numbers among the first 10,000 positive integers.

376 = 17 + 35 + 53 + 71.

Source: Number Gossip

## Tuesday, March 26, 2013

### 1472

1472 = 2 x 2 x 2 x 2 x 2 x 2 x 23.

-1472 is the fourth value of the Ramanujan tau function (A000594).

1472 is a divisor of 474 - 1.

23 x 64 = 1472 = 32 x 46.

The number of prime numbers of the form 4n +1 less than 26,861 equals the number of prime numbers of the form 4n + 3 less than 26,861: 1472.

Source: Numeropedia

## Monday, March 25, 2013

### 7607

7607 is a prime number.

7607 is 1110110110111 in base 2 (binary) (A016041). It is 101102202 in base 3 (A174976) and 1312313in base 4.

7607 is the lower prime of a difference of 14 between consecutive primes (A031932).

7607 and the reversal of 76078 are both primes (A059701). 7607 and 607 are both primes (A167187).

Source: On-Line Encyclopedia of Integer Sequences

## Friday, March 22, 2013

### 782

782 = 2 x 17 x 23.

782 is a pentagonal number (A000326).

782 is a number whose sum of divisors is a fourth power (A006532): 1 + 2 + 17 + 23 + 34 + 46 + 391 + 782 = 1296 = 64.

The sum of the squares of the first 782 primes is a prime (A098561).

782 is a divisor of 474 - 1.

Source: Number Gossip

## Thursday, March 21, 2013

### 467

467 is a prime number.

467 is the smallest prime p in which the concatenation of p with the next prime remains prime throughout two steps of the same procedure. For example, 467 concatenated with the next prime (479) gives the prime 467479, and 467479 concatenated with the next prime (467491) gives the prime 467479467491. 467 is also the smallest whose successive concatenations remain prime throughout three steps.

467 has strictly increasing digits in bases 7 (1235), 9 (568), and 10 (467).

467 is a safe prime (A005385).

The sum of the digits of 467 is a prime (A046704).

Source: Prime Curios!

## Wednesday, March 20, 2013

### 7451

7451 is a prime number.

7451 is the upper prime of a difference of 18 between consecutive primes (A031937). It is also the larger of two consecutive primes whose sum is a square (A118591): 7433 + 7451 = 14884 = 1222.

7451 is palindromic in base 7 (A029975): 30503.

7451 can be expressed as the sum of consecutive primes in exactly four ways (A054999).

7451, 7457, and 7459 are primes, but 7453 is not (A049438).

7451 is a prime congruent to 22 mod 23 (A141926).

Source: On-Line Encyclopedia of Integer Sequences

## Tuesday, March 19, 2013

### 763

763 = 7 x 109.

763 is the smallest number whose fourth power (7634 = 338920744561) contains all the digits from 0 to 9 at least once.

763 is 3311 in base 6.

763 is the sum of nine consecutive primes: 763 = 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103.

Source: Number Gossip

## Monday, March 18, 2013

### 997

997 is a prime number. It is the largest three-digit prime.

997 is the smallest prime of the form 10p - p, where p is prime (3).

997 is the smallest prime whose sum of digits (25) is an odd composite number.

997 is the smallest prime p such that the sum of the digits of p (9 + 9 + 7 = 25) is not prime, but the sum of the squares of the digits is prime (92 + 92 + 72 = 211).

997 is the smallest prime p such that the sum of the digits of p (9 + 9 + 7 = 25) is not prime, but the sum of the cubes of the digits is prime (93 + 93 + 73 = 1801).

997 has a representation as a sum of two squares: 997 = 62 + 312.

997 is the hypotenuse of a primitive Pythagorean triple: 9972 = 3722 + 9252.

Sourcea: Number Gossip and Prime Curios!

## Friday, March 15, 2013

### 2042

2042 = 2 x 1021.

2042 is palindromic in base 3: 2210122.

2042 has a representation as a sum of two squares: 2042 = 192 + 412.

The digits of 2042 are not present among the digits of 20424 = 17386931815696 (A111116).

In 1948, the candela was defined as the luminous intensity of 1/600,000 of a square meter of a cavity at the temperature of freezing platinum, 2042 kelvins.

Source: On-Line Encyclopedia of Integer Sequences

## Thursday, March 14, 2013

### 657

657 = 3 x 3 x 73.

657 is 1010010001 in base 2 (binary). It is 1221 in base 8.

657 has a representation as a sum of two squares: 657 = 92 + 242.

657 is the largest known integer that cannot be written as the sum of a semiprime and a square.

657 is the number of ways to tile a 4 x 22 rectangle with 4 x 1 rectangles.

657 = 219 + 438 uses each of the digits from 1 to 9 once.

Source: Prime Curios!

## Wednesday, March 13, 2013

### 350

350 = 2 x 5 x 5 x 7.

350 is a divisor of 992 - 1.

350 is 1010 in base 7. It is 252 in base 12.

350 is a Stirling number of the second kind S(7,4) (A008277).

1 + 3501 + 3502 + 3503 + 3504 + 3505 + 3506 is a prime (A100330).

The sum of the first 350 primes (379667) is a prime (A013916).

Source: On-Line Encyclopedia of Integer Sequences

## Tuesday, March 12, 2013

### 1733

1733 is a prime number. It is a Sophie Germain prime because 2 x 1733 + 1 = 3467 is also prime.

1733 is the smallest prime that contains exactly six smaller primes as substrings: 3, 7, 17, 73, 173, 733.

1733 is palindromic in base 3: 2101012. It is 565 in base 18.

1733 has a representation as a sum of two squares: 1733 = 172 + 382.

1733 is the hypotenuse of a primitive Pythagorean triple: 17332 = 11552 + 12922.

## Monday, March 11, 2013

### 830

830 = 2 x 5 x 83. It is the product of three distinct Sophie Germain primes (A157346).

830 is 1010202 in base 3. It is 434 in base 14.

830 is the sum of four consecutive primes (A034963): 830 = 197 + 199 + 211 + 223.

830 is the sum of 11 positive fifth powers (A003356).

830 incremented by the sum of its digits (8 + 3 + 0 = 11) produces a square (A066564): 830 + 11 = 841 = 292.

In the year 830 Persian mathematician Al-Khworizmi, working at the House of Wisdom in Baghdad, developed what came to be known as algebra in his work Hisab al-jabr w'al-muqabala.

Source: On-Line Encyclopedia of Integer Sequences

## Friday, March 8, 2013

### 956

956 = 2 x 2 x 239.

956 is the number of multigraphs with 16 vertices and 4 edges (A003082).

956 is 678 in base 12.

956 and 9562 (913,936) have the same initial digits and the same final digits (A086457).

956 and the 956th prime (7541) have only the digit 5 in common (A107936).

## Thursday, March 7, 2013

### 550

550 = 2 x 5 x 5 x 11.

550 is a pentagonal pyramidal number (A002411).

505 is 202101 in base 3. It is 1414 in base 7.

550 is the number of primes less than 4000 (A028505 and A038812).

550 is a divisor of 434 - 1.

## Wednesday, March 6, 2013

### 1712

1712 = 2 x 2 x 2 x 2 x 107.

1712 is the number of regions into which the complex plane is cut by drawing lines between all pairs of 16th roots of unity (A006533).

1712 is 4664 in base 7.

1712 is the sum of eight consecutive primes (A127335): 1712 = 193 + 197 + 199 + 211 + 223 + 227 + 229 + 233.

Each digit of 1712 occurs at least once in 17124 = 8,590,432,731,136 (A121321).

## Tuesday, March 5, 2013

### 823

823 is a prime number.

821 and 823 form a twin prime pair. 823 forms a prime quadruplet with 821, 827, and 829.

823 = 12345/(1 + 2 + 3 + 4 + 5).

823 is a number that does not have any digits in common with its cube (557441767).

Victor Hugo's novel Les Misérables contains a sentence of 823 words, one of the longest sentences in the French language.

Source: Prime Curios!

## Monday, March 4, 2013

### 1700

1700 = 2 x 2 x 5 x 5 x 17.

1700 is 11010100100 in base 2 (binary).

1700 is the generalized Catalan numer C(13, 4) (A039598).

1700 is 4646 in base 7. It is 2288 in base 9 and A0A in base 13.

1700 has three representations as a sum of two squares (A000443): 1700 = 102 + 402 = 162 + 382 = 262 + 322.

## Friday, March 1, 2013

### 4633

4633 = 41 x113.

4633 is a number such that each digit leaves the same nonzero remainder when each is divided into the number (A152824).

4633 is a number n such that 15n - 4, 15n - 2, 15n + 2, and 15+ 4 form a prime quadruplet (A112540).

4633 is a divisor of 448 - 1.

4633 has two representations as a sum of two squares: 4633 = 32 + 682 = 122 + 672.

4633 is the hypotenuse of two primitive Pythagorean triples: 46332 = 4082 + 46152 = 16082 + 43452.

Source: On-Line Encyclopedia of Integer Sequences