Friday, May 31, 2013

399

399 = 3 x 7 x 19.

399 is 333 in base 11.

399 is the total number of parts in all partitions of 12.

399 is the smallest Lucas-Carmichael number.

399 = 71 + 72 + 73.

399 is the smallest number, all of whose prime factors are of the form 4n + 3, whose sum of distinct prime factors is prime (3 + 7 + 19 = 29).

399 is the sum of 11 consecutive primes: 399 = 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59.

Source: Number Gossip

Thursday, May 30, 2013

608

608 = 2 x 2 x 2 x 2 x 2 x 19.

608 is a number that has no digits in common with its cube (224,755,712).

608 is 211112 in base 3 (A014190).

608 is the number of 3 x 3 magic squares (with distinct positive entries) having all entries less than 21 (A108576).

608 is the smallest of three consecutive integers (608, 609, 610) divisible by three consecutive primes, respectively (A073607).

Wednesday, May 29, 2013

906

906 = 2 x 3 x 151.

906 is the number of perfect graphs with 7 vertices.

906 = 25 x 33 + 42.

906 is an even number that is not the sum of a pair of twin primes (A007534).

906 is a number n such that the concatenation 2n3n5n7n11n13 is a prime (A092117).

906 is a strobogrammatic cyclops number (A153806).

Tuesday, May 28, 2013

1474

1474 = 2 x 11 x 67.

1474 is a member of a Fibonacci-like sequence starting with 2 and 9.

1474 is the difference between the product of two consecutive primes and the next prime (A111071).

1474 has the property that all pairs of consecutive digits differ by 3 (A033081).

1474 is pandigital in Roman numerals (MCDLXXIV). It uses each of the symbols I, V, X, L, C, and M at least once (A105417).

Friday, May 24, 2013

690

690 = 2 x 3 x 5 x 23.

690 is the smallest number that can be written as the sum of a triangular number, a cube, and a Fibonacci number.

690 is the sum of six consecutive primes: 690 = 103 + 107 + 109 + 113 + 127 + 131.

690 has the representation 690 = 36 - 39.

690 is a divisor of 912 - 1.

Thursday, May 23, 2013

1337

1337 = 7 x 191.

1337 is a number with exactly two palindromic prime factors and no other prime factors (A046368).

1337 is the smallest number m such that reversal of m1000 is prime.

1337 is a multiple of 7 such that its digit sum (1 + 3 + 3 + 7 = 14) is divisible by 7 (A216994).

1337 is the product of two distinct primes a and b such that a + b is the average of a twin prime pair (A176875): 7 + 191 = 198 = (197 + 199)/2.

1337 is the average of three successive primes, each squared (A075893).

1337 is a multiple of 7 containing only odd digits (A061825).

1337 is a divisor of 3915 - 1.

1137 Gerarda is an asteroid discovered in 1934.

Leet (or "1337") is an alternative alphabet for the English language that is used mainly on the Internet.

Source: Number Gossip

Wednesday, May 22, 2013

862

862 = 2 x 431.

862 is a number whose sum of divisors is a fourth power: 1 + 2 + 431 + 862 = 1296 = 64.

862 is the maximum number of regions into which 41 lines divide the plane.

862 has the representation 862 = 25 x 33 - 2.

862 is a divisor of 955 - 1.

Tuesday, May 21, 2013

2220

2220 = 2 x 2 x 3 x 5 x 37.

2220 is a divisor of 314 - 1.

2220 is a multiple of six and the sum of its digits is also six (A062768).

2220 is the sum of even numbers in the range 440 to 449 (A053741).

2220 is the number of partitions of 36 into powers of 6 (A196884).

2220 is a year in which the month of February has five Tuesdays (A143994).

Source: On-Line Encyclopedia of Integer Sequences

Monday, May 20, 2013

1401

1401 = 3 x 467.

1401, 1402, and 1403 are each the product of two primes (semiprimes) (A056809). 1401, 1403, and 1405 are each the product of two primes (A092125).

1401 is a composite number such that every concatenation of its prime factors (3467 and 4673) is prime (A217263).

1401 is the number of 8-digit primes that can be represented as sums of consecutive squares (A218213).

1401 in base 6 (10253) has five distinct digits (A031983).

Source: On-Line Encyclopedia of Integer Sequences

Friday, May 17, 2013

761

761 is a prime number. It is a Sophie Germain prime because 2 x 761 + 1 = 1523 is also prime.

761 is a centered square number.

761 is the sum of all primes numbers up to 79.

761 has a representation as a sum of two squares: 761 = 192 + 202.

761 is the hypotenuse of a primitive Pythagorean triple: 7612 = 392 + 7602.

A sequence of six nines (known as the Feynman point) begins immediately after the 761st decimal place of pi. Physicist Richard Feynman expressed a wish to memorize the digits of pi as far as that point so that when reciting them he would be able to end with ". . . nine, nine, nine, nine, nine, nine, and so on."

Source: Prime Curios!

Thursday, May 16, 2013

341

341 = 11 x 31.

341 is 101010101 in base 2 (binary). It is 11111 in base 4.

341 is an octagonal number and a centered cube number.

341 is the first composite number to disprove an ancient Chinese conjecture (circa 500 B.C.) that n is a prime number if and only if n divides the number 2n - 2. The number 2341 - 2 is divisible by 341, a composite number. 341 is the smallest pseudoprime in base 2.

341 is the sum of seven consecutive primes: 341 = 37 + 41 + 43 + 47 + 53 + 59 + 61.

341 = 40 + 41 + 42 + 43 + 44.

341 is the smallest number with seven representations as a sum of three positive squares: 341 = 12 + 42 + 182 = 12 + 122 + 142 = 22 + 92 + 162 = 42 + 62 + 172 = 42 + 102 + 152 = 62 + 72 + 162 = 82 + 92 + 142.

Source: Number Gossip

Wednesday, May 15, 2013

734

734 = 2 x 367.

734 is the smallest number that can be written as the sum of three distinct non-zero squares in ten ways.

734 is the sum of eight positive fifth powers (A003353).

734 is the number of hexagons that can be formed with perimeter 34 (A069907).

734 is the sum of 14 but no fewer nonzero fourth powers (A046045).

734 has the representation 734 = 36 + 5.

734 is a divisor of 833 - 1.

Tuesday, May 14, 2013

971

971 is a prime number.

971 is the largest prime containing only odd digits, in decreasing order.

971 is the largest prime formed from the concatenation of a one-digit composite number, one-digit prime number, and one-digit number that is neither prime nor composite.

971, 719, and 197 are all primes.

971 is the smallest of three consecutive primes with a difference of six; a prime p such that p (971), p + 6 (977), and p + 12 (983) are all primes (A047948).

Source: Prime Curios!

Monday, May 13, 2013

5038

5038 = 2 x 11 x 229.

5038 is the sum of two distinct prime cubes (A120398): 5038 = 173 + 53.

5038 is the least nontrivial multiple of the 50th prime (229) beginning with 5 (A078289).

5038 is a number n such that n2 (25381444) ends in 444 (A039685).

5038 is the difference of between two factorial numbers (A051949).

Source: On-Line Encyclopedia of Integer Sequences

Friday, May 10, 2013

556

556 = 2 x 2 x 139.

556 is the total number of parts in all partitions of 13.

556 are the first three digits of 4556.

556 is the sum of four consecutive primes: 556 = 131 + 137 + 139 + 149.

556 is an untouchable number; it is never the sum of the proper divisors of any integer.

556 Phyllis is an asteroid orbiting the sun, discovered in 1905.

U-556 was a German submarine that was built for and operated during World War II.

Thursday, May 9, 2013

1771

1771 = 7 x 11 x 23.

1771 is the smallest of three consecutive numbers that are products of exactly three primes (A113789).

1771 is the 21st tetrahedral number (A000292).

1771 is the concatenation of the 7th prime (17) and its reverse (71) (A067087).

1771 is a divisor of 456 - 1.

1771 is a number n such that n2 (3136441) is a concatenation of two nonzero squares (A048375): 3136 = 562 and 441 = 212.

Source: Number Gossip

Wednesday, May 8, 2013

1573

1573 = 11 x 11 x 13.

1573 is a value of n for which n, 2n, 3n, and 4n all use the same number of digits in Roman numerals.

1573 is a number n for which 10n + 1, 10n + 3, 10n + 7, and 10n + 9 are primes (A007811).

1573 is the sum of the remainders when the 48th prime (223) is divided by primes up to the 47th prime (211) (A033955).

1573 is a concentric tridecagonal number (A195045).

1573 is a divisor of 275 - 1.

1573 has a representation as a sum of two squares: 1573 = 222 + 332.

Tuesday, May 7, 2013

585

585 = 3 x 3 x 5 x 13.

585 is 1001001001 in base 2 (binary) and 1111 in base 8. It is a palindrome in base 2, base 8, and base 10.

585 is the number of integer partitions of 35 into distinct parts.

585 has two representations as a sum of two squares: 585 = 32 + 242 = 122 + 212.

585 is a divisor of 642 - 1.

Monday, May 6, 2013

9966

9966 = 2 x 3 x 11 x 151. It has exactly four distinct palindromic prime factors (A046402).

9966 is the largest four-digit strobogrammatic number (A000787).

9966 is a number m such that (6 x m)5 is a sum of a twin prime pair (A173560).

9966 is an integer of the form 1/3 + 2/3 + 3/3 + 5/3 + 7/3 + 11/3 + 13/3 + 17/3 + ... (A182155).

Friday, May 3, 2013

984

984 = 2 x 2 x 2 x 3 x 41.

984 is a divisor of 832 - 1.

984 = 8 + 88 + 888.

984 is a number n such that 1 + n + n3 + n5 + n7 + . . . + n23 + n25 + n27 is a prime (A124185).

984 are the final three digits of 254 (A126605).

Thursday, May 2, 2013

470

470 = 2 x 5 x 47.

470 is a cake number, the maximum number of pieces into which a cylindrical cake can be cut with 14 straight-plane cuts (A000125).

470 has a base 3 representation (122102) that ends with its base 6 representation (2102).

470 is the sum of the first 24 non-primes (A051349).

470 is a number n such that its square (220900) is a sum of two successive primes (A074294).

Source: Number Gossip

Wednesday, May 1, 2013

1534

1534 = 2 x 13 x 59.

1534 is 4321 in base 7.

1534 arises in the sequence generated by starting with 1 then successively doubling the number and adding 1 to the result (A083416).

1534 has exactly nine 1s in its binary expansion (A023961).

1534 is the sum of the first 37 primes minus the sum of the first 37 non-primes (A071411).