## Wednesday, April 30, 2014

### 2695

2695 = 5 x 7 x 7 x 11 (A036490).

2695 and its digit sum are both multiples of 11 (A216995).

2695 is a number for which its smallest and largest prime factors differ by 6 (A195118).

2695 is 3624 in base 9 and 2030 in base 11.

The 2695th prime minus 2695 gives a triangular number (A115883).

2695 divides 6712 - 1.

2695 is a number that cannot be written as a sum of three squares.

Source: OEIS

## Tuesday, April 29, 2014

### 3639

3639 = 3 x 1213.

Concatenating the distinct prime factors of 3639 produces a palindrome (A046448): 31213.

3639 is a member of the Fibonacci-like sequence beginning with 1 and 15 (A022105).

The square of 3639 contains only the digits 1, 2, 3, and 4 (A061677).

3639 divides 4712 - 1.

3639 is a number that cannot be written as a sum of three squares.

Source: OEIS

## Monday, April 28, 2014

### 6623

6623 = 37 x 179.

6623 has the property that the sum of its prime factors is equal to the product of its digits (A067173).

6623 is a centered heptagonal number (A069099).

6623 is a number n such that the nth and the (n + 1)th primes have the same sum of their digits squared (A109182).

6623 is a member of the Fibonacci-like sequence beginning with 12 and 67 (A091074).

6623 is a number that cannot be written as a sum of three squares.

## Friday, April 25, 2014

### 8809

8809 = 23 x 383.

8809 is the 103 lucky number (A181382).

The last four digits of 8809 in base three (110002021) match the first four digits of 8809 in base 4 (2021221).

8809 is a number n such that n times n + 9 gives the concatenation of two numbers m and m - 5 (A116258).

Source: OEIS

## Thursday, April 24, 2014

### 5535

5535 = 3 x 3 x 3 x 5 x 41.

Every digit of 5535 is a prime factor of 5535 (A062239).

5535 and the square of 5535 use only the digits 0, 2, 3, 5, and 6 (A136888).

5535 is a number n such that n3 - 4 and n3 + 4 are prime (A161589).

5535 is a number n such that (n3 + 2 and n3 + 4) is a twin prime pair (A178337).

5535 divides 7312 - 1.

5535 is a number that cannot be written as a sum of three squares.

Source: OEIS

## Wednesday, April 23, 2014

### 8940

8940 = 2 x 2 x 3 x 5 x 149.

8940 is 3388 in base 14.

8940 is a number n such that n + 1, 2n + 1, and n2 + 1 are primes (A236692).

8940 is the number of subsets of {1, 2, . . ., 38} containing 38 and having less than or equal to nine pairwise coprime elements (A186993).

8940 is the number of arrays of squares of integers, symmetric under 90-degree rotation, with all rows summing to 2 (A156411).

Source: OEIS

## Tuesday, April 22, 2014

### 4774

4774 = 2 x 7 x 11 x 31. It is a palindrome with exactly four prime factors (A046330).

4774 is a heptagonal number (A000566).

4774 is a multiple of 11 and its digit sum is a multiple of 11 (A216995).

4774 is the concatenation of the 15th prime and its reverse (A067087).

4774 is 34034 in base 6 and 2233 in base 13 (A033011).

4774 divides 673 - 1.

Source: OEIS

## Monday, April 21, 2014

### 5769

5769 = 3 x 3 x 641.

5769 is the number of permutations of nine elements that have a third power equal to the identity permutation (A001470).

5769 is the number of binary strings of length 14 with no substrings equal to 0001 or 1000 (A164398).

5769 has a representation as a sum of two squares: 5679 = 122 + 752.

5769 divides 10016 - 1.

5769 is the number of (unordered) ways of making change for n cents using coins of 1/2, 1, 2, 3, 5, 10, 20, 25, 50, and 100 cents (all historical U.S. coinage denominations up to 100 cents (A067997).

## Friday, April 18, 2014

### 6097

6097 = 7 x 13 x 67. It is the product of three distinct non-Sophie Germain primes (A157347) and the product of three distinct primes of the form 6n + 1 (A154729).

6097 is a hexagonal prism number (A005915).

6097 is an alternating sum of decreasing powers (A083327).

6097 is the half-sum (or average) of the cubes of two distinct odd primes (A138855).

6097 divides 293 - 1.

## Thursday, April 17, 2014

### 1813

1813 = 7 x 7 x 37.

1813 is the sum of the first 35 semiprimes (A062198).

1813 is the number of trees on 15 vertices with diameter 8.

1813 is 12221 in base 6.

1813 has a representation as a sum of two squares: 1813 = 72 + 422.

1813 divides 486 - 1.

## Wednesday, April 16, 2014

### 1782

1782 = 2 x 3 x 3 x 3 x 3 x 11.

1782 is a heptagonal number.

1782 is the smallest number that is three times the sum of all the two-digit numbers that can be made using the digits of 1782.

1782 is the smallest number n such that n and 4n (7128) are anagrams.

1782 is 3366 in base 8.

1782 divides 8918 - 1.

Source: Number Gossip

## Tuesday, April 15, 2014

### 1693

1693 is a prime number.

1693 is a prime that results from merging four successive digits in the decimal expansion of pi (A104824).

1693 is a prime whose binary representation (11010011101) is also the decimal representation of a prime (A065720).

1693 is the smallest prime greater than 412 (A007491).

1693 has a representation as a sum of two squares: 1693 = 182 + 372.

1693 is the hypotenuse of a primitive Pythagorean triple: 16932 = 10452 + 13322.

1693 divides 924 - 1.

Pope Clement XIII was born in the prime year 1693; he was the most recent pope to be born in a prime year.

Source: Prime Curios!

## Monday, April 14, 2014

### 2433

2433 = 3 x 811.

2433, 2434, and 2435 are consecutive semiprimes, each the product of two primes (A056809).

2433 is 3303 in base 9.

2433 is the sum of three distinct powers of three (A038465).

2433 is the arithmetic mean of five successive primes (A219505).

2433 divides 727 - 1.

Source: OEIS

## Friday, April 11, 2014

### 7533

7533 = 3 x 3 x 3 x 3 x 3 x 31.

7533 is a number whose prime divisors (3 and 31) are all Mersenne primes (A056652).

7533 is the difference of two positive fifth powers (A181124).

7533 is a number n such that 12n + 1, 12n + 5, 12n + 7, and 12n + 11 are primes (A123985).

7533 divides 8215 - 1.

Source: OEIS

## Thursday, April 10, 2014

### 5137

5137 = 11 x 467.

5137 is a semiprime whose digit reversal is a pentagonal number (A115708).

5137 is 1010000010001 in base 2 (binary) and 1100101 in base 4. 5137 is 21001021 in base 3 and 12021 in base 8.

5137 is the number of 4-bead necklaces labeled with numbers -19 . . . 19 allowing reversal, with sum zero with no three beads in row equal (A209345).

5137 is the sum of four distinct powers of 4 (A038472).

Source: OEIS

## Wednesday, April 9, 2014

### 2984

2984 = 2 x 2 x 2 x 373.

2984 is the number of different products of subsets of the set {1, 2, 3, . . . 15} (A060957).

2984 is the number of triangles in all dissections of a convex octagon by nonintersecting diagonals (A089382).

2984 is 1888 in base 12.

2984 is the sum of nine nonzero 6th powers (A003365).

2984 has a representation as a sum of two squares: 2984 = 222 + 502.

2984 divides 896 - 1.

## Tuesday, April 8, 2014

### 5845

5845 = 5 x 7 x 167.

5845 is the product of three distinct safe primes (A157354).

5845 is the number of squares on a infinite half chessboard at less than or equal to 29 knight moves from a fixed point on the diagonal (A098499).

5845 is a number n such that n2 + 1 and (n + 1)2 + 1 are each divisible by a square (A217798).

5845 in base 11 is made up of only the digits 3 and 4 (4434) (A032835). 5845 and the square of 5845 in base 6 (43021 and 3220130441) use the same digits in the same proportion (A061660).

Source: OEIS

## Monday, April 7, 2014

### 6680

6680 = 2 x 2 x 2 x 5 x 167.

6680 = 6666 + 6 + 8 + 0.

6680 is the number of essentially different ways in which the squares 1, 4, 9, . . . 162 can be arranged in a sequence such that all pairs of adjacent squares sum to a prime number (rotations and reversals are counted only once) (A073451).

6680 and the square of 6680 (44622400) use only the digits 0, 2, 4, 6, and 8 (A136904).

6680 is a number n such that n2, n2 + 1, and n2 + 2 are all semiprimes (A179502).

## Friday, April 4, 2014

### 9202

9202 = 2 x 43 x 107.

9202 is palindromic in base 4: 2033302. It ends in 554 is base 7 (35554) and base 9 (13554).

9202 is a number n such that n!!!!! + 1 is prime (A085148).

Any two consecutive digits of 9202 sum up to a prime (A158652).

9202 is the volume of sphere (rounded down) with radius 26 (A228272).

Source: OEIS

## Thursday, April 3, 2014

### 1112

1112 = 2 x 2 x 2 x 139.

1112 has a base 3 representation that begins with 1112.

1112 is divisible by the product of its digits (A007602). The product of its digits is a prime (A028842).

1112 times its reversal, 2111, produces a palindrome (A043344): 1112 x 2111 = 2347432.

1112 divides 436 - 1.

## Wednesday, April 2, 2014

### 8490

8490 = 2 x 3 x 5 x 283.

8490 is the number of compositions of 22 into 5 ordered relatively prime parts (A000743).

8490 is the number of base 14 7-digit numbers with adjacent digits differing by one or less (A126368).

8490 is a number n for which n' + n and n' - n are both prime, n' being the arithmetic derivative of n (A229272).

8490 is the total number of parts in all partitions of 37 into odd parts (A067588).

8490 is the conjectured lower bound for the number of spheres of radius 1 that can be packed in a sphere of radius 23 (A121346).

Source: OEIS

## Tuesday, April 1, 2014

### 3009

3009 = 3 x 17 x 59.

3009 is a number with prime factors a, b, and c such that a + b + c, a2 + b2 + c2, and a3 + b3 + c3 are all primes (A176911).

3009 divides 5816 - 1.

3009 is a member of the crystal ball sequence for hexagonal close-packing (A007202).

Source: OEIS