## Friday, December 23, 2011

### 2012

2012 = 22 x 503.

2012, 2013, 2014, and 2015 are each the product of three prime numbers.

2012! has a square number of digits (5776 = 762).

20122 = 4048144 and 4418404 = 21022.

2012 and its square (4048144) use only the digits 0, 1, 2, 4, and 8.

2012 is a year in which there are five Wednesdays in the month of February.

2012 is a blue moon year.

The end of the "longest period" (Long Count) Mayan calendar known to exist is said to be December 21, 2012.

2012 is the 100th anniversary of the sinking of the RMS Titanic. It is also the centennial of the birth of Alan Turing.

## Thursday, December 22, 2011

### 524

524 = 22 x 131.

524 is a divisor of 535 - 1.

6 x 7 x 9 x 524 x 831 = 164,597,832 uses each of the digits from 1 to 9 once on both sides of the equality.

524 is 201102 (palindromic) in base 3.

The USS Pickerel (USN-524) was a submarine commissioned in 1949.

## Wednesday, December 21, 2011

### 1011

1011 = 3 x 337.

1011 is the smallest number without trailing zeroes such that the reversal of its cube is the cube of a different number (1101).

1011 has a square that is formed by inserting three 2s into it: 10112 = 1022121.

1011 is 323 (palindromic) in base 18. 1011 has a representation ending in 3 in base 4, 6, 7, 8, 9, 12, 14, and 18.

The Nokia 1011 was the first mass-produced GSM phone.

## Tuesday, December 20, 2011

### 107

107 is a prime number.

107 is 1101011 in base 2 (binary).

107 and 109 form a twin prime pair.

2107 - 1 is a Mersenne prime.

107 is the smallest three-digit prime that remains a prime when 2 is added to any one of its digits: 307, 127, and 109 are all primes.

107 is the maximum number of steps that a four-state Turing machine can make on an initially blank tape before it halts.

107 Camilla is one of the largest main-belt asteroids.

Source: Prime Curios!

## Monday, December 19, 2011

### 383

383 is a prime number. It is a sexy prime because 383 + 6 = 389 is also prime.

383 is the only known multidigit palindromic Woodall prime.

383 is the sum of the first three three-digit palindromic primes: 383 = 101 + 131 + 151.

383 is the smallest prime that can be represented by the sum of a prime and its reversal: 383 = 241 + 142.

383 is a divisor of the Mersenne number 2191 - 1.

The Chevy 383 stroker engine uses an altered crankshaft to increase the stroke of the pistons.

## Friday, December 16, 2011

### 967

967 is a prime number. 967 in reverse is the prime 769.

967 is a divisor of 977 - 1.

967 is the number of six-digit triangular numbers.

967 is 595 in base 13.

967 millimeters is the record for annual rainfall in Melbourne, Australia, set in 1916.

## Thursday, December 15, 2011

### 743

743 is a prime number. It is a Sophie Germain prime because 2 x 743 + 1 = 1487 is a prime.

743 is the number of independent sets of the graph of the tesseract (four-dimensional cube).

6487 + 1399684 = 75582723.

743 is 616 in base 11 and 212 in base 19.

The sun's mass is about 743 times the combined mass of all the planets in the solar system.

## Wednesday, December 14, 2011

### 1352

1352 = 23 x 132.

1352 has two representations as a sum of two squares: 1352 = 142 + 342 = 262 + 262.

1352 is a divisor of 994 - 1.

1352 is 20402 in base 5 and 242 in base 25. It is 800 in base 13 and 200 in base 26.

NGC 1352 is a barred spiral galaxy in the constellation Eridanus.

## Tuesday, December 13, 2011

### 197

197 is a prime number.

197 is the sum of the first 12 primes: 197 = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37. It is also the smallest prime that is the sum of seven consecutive primes: 197 = 17 + 19 + 23 + 29 + 31 + 37 + 41.

197 is the sum of the digits of all two-digit primes.

197 is the sum of the squares of all composite digits: 197 = 42 + 62 + 82 + 92.

197 has a representation as a sum of two squares: 197 = 12 + 142.

197 and 199 form a twin prime pair.

197 is the hypotenuse of a primitive Pythagorean triple: 1972 = 282 + 1952.

The chemical element gold has one stable isotope, which has a total of 197 neutrons and protons in its nucleus.

## Monday, December 12, 2011

### 647

647 is a prime number.

647 is a divisor of 4317 - 1.

647 is the smallest prime that can be written as 2a2 - 1 and as 3b3 - 1.

647 is 343 in base 14.

647 is the sum of five consecutive primes: 647 = 113 + 127 + 131 + 137 + 139.

Tremont 647 is a restaurant in Boston.

## Friday, December 9, 2011

### 286

286 = 2 x 11 x 13.

286 is the 11th tetrahedral number.

286 is the number of rooted trees with 9 vertices.

286 is 2121 in base 5 and 141 in base 15.

286 is the shorthand for the Intel 80286 microprocessor chip.

## Thursday, December 8, 2011

### 360

360 = 23 x 32 x 5.

360 has a representation as a sum of two squares: 360 = 62 + 182.

360 is the largest number out of two (the other being 36) that have the same number of letters in its Roman numeral representation (CCCLX) as its double (DCCXX), triple (MLXXX), quadruple (MCDXL), quintuple (MDCCC), sextuple (MMCLX), and septuple (MMDXX).

360 is the smallest number divisible by every natural number from 1 to 10 except 7.

One of the divisors of 360 is 72, which is the number of prime numbers less than 360.

360 is the sum to two twin primes: 360 = 179 + 181.

360 is the number of degrees in a circle.

## Wednesday, December 7, 2011

### 939

939 = 3 x 313.

939 is a divisor of 254 - 1.

939 has a cube root whose decimal part starts with the digits 1 to 9 in some order: 9.792386145. . .

939 is 32223 in base 4 and 12224 in base 5.

939 is a number n such that n - 2 and n + 2 are consecutive primes: 937 and 941.

The Berklee College of Music's Cafe 939 is a student-run music venue and coffeehouse.

## Tuesday, December 6, 2011

### 175

175 = 52 x 7.

175 is a divisor of 762 - 1.

175 = 11 + 72 + 53.

175 is the smallest number n such that n6 + 6 is prime.

Emory University was 175 years old in the year 2o11.

## Monday, December 5, 2011

### 831

831 = 3 x 277.

6 x 7 x 9 x 524 x 831 = 164,597,832 (using each of the nine digits 1 to 9 on both sides of the equality).

831 is a divisor of 3512 - 1.

831 is 11311 in base 5 and 696 in base 11.

831 is the sum of 12 positive fifth powers: 831 = 35 + 35 + 35 + 25 + 25 + 25 + 15 + 15 + 15 + 15 + 15 + 15.

831 stands for "I love you": eight letters, three words, one meaning.

Source: Numeropedia

## Friday, December 2, 2011

### 342

342 = 2 x 32 x 19.

342 is 666 in base 7. It is the smallest number that can be represented by 666 in any base. 342 is also 2332 in base 5.

342 is the number of inequivalent binary linear codes of length 8.

IC 342 (also known as Caldwell 5) is a spiral galaxy in the constellation Camelopardalis.

## Thursday, December 1, 2011

### 727

727 is a prime number.

727 is the smallest prime of the form n3 - 2.

727 = 1! + (1 + 2)! + (1 + 2 + 3)!

727 is the smallest odd prime that can be represented as the sum of a cube and its reversal: 727 = 83 + 215 = 512 + 215.

727 is the first prime whose square (528529) can be represented as the concatenation of two consecutive numbers.

The Boeing 727 was the first three-engine jet built for commercial service.

## Wednesday, November 30, 2011

### 1226

1226 = 2 x 613.

1226 has a representation as a sum of two squares: 1226 = 12 + 352.

1226 is 14401 in base 5 and 3401 in base 7.

1226 is a divisor of 653 - 1.

1226 is a central polygonal number (lazy caterer's sequence), or the maximum number of pieces formed when slicing a pancake with 49 cuts.

The Stone Circles of Senegambia is site 1226 on the UNESCO World Heritage list.

## Tuesday, November 29, 2011

### 147

147 = 3 x 72.

147 is the number of one-sided 6-polyhexes.

147 = 142 - 72 = (14 + 7)7.

147(14 + 7) = 143 + 73 = 3087.

147 is 300 in base 7, 77 in base 20, and 70 in base 21. It is 2103 in base 4, 403 in base 6, and 103 in base 12 (and 93 in base 16, 83 in base 18, and 63 in base 24).

The binary form of 147 (10010011) contains all two-digit binary numbers (00, 01, 10, and 11) in a sequence.

The digits forming 147 also form the left-hand column of a normal decimal keypad.

## Monday, November 28, 2011

### 619

619 is a prime number.

617 and 619 form a twin prime pair.

619 = 6! - 5! + 4! - 3! + 2! - 1!

619 is the only strobogrammatic prime with distinct digits. It is the smallest strobogrammatic prime that is not a palindrome.

Nova 619 is a webcomic.

## Wednesday, November 23, 2011

### 834

834 = 2 x 3 x 139.

834 is a divisor of 436 - 1.

834 is a cake number. 834 is the maximum number of regions into which 17 cuts can divide a cube.

834 is the sum of six consecutive primes: 834 = 127 + 131 + 137 + 139 + 149 + 151.

The Volvo PV834 was one of a series of commercial vehicles, including ambulances, produced in the 1950s.

## Tuesday, November 22, 2011

### 132

132 = 22 x 3 x 11.

The sum of all two-digit numbers that you can make from 132 is 132: 12 + 13 + 21 + 23 + 31 + 32 = 132. It is the smallest number with this property.

132 is the sixth Catalan number.

132 is a divisor of 232 - 1.

The game board for Indian snakes and ladders (Moksha Patamu) has 132 squares.

## Monday, November 21, 2011

### 225

225 = 32 x 52.

225 = 152. 225 is the smallest square that starts with two identical digits.

225 is the smallest square whose external digits (25) form a square, and whose internal digits (2) form a prime.

225 is the only three-digit square with all prime digits.

225 has a representation as a sum of two squares: 225 = 92 + 122.

225 is a divisor of 262 - 1.

225 is an octagonal number. It is also a centered octagonal number.

A Scrabble board has 225 squares.

## Friday, November 18, 2011

### 928

928 = 25 x 29.

928 has a representation as a sum of two squares: 928 = 122 + 282.

928 is the sum of four consecutive primes: 928 = 227 + 229 + 233 + 239. It is also the sum of eight consecutive primes: 928 = 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137.

928 is the number of ways to toss a coin 10 times and not get a run of six.

The Porsche 928 was a sports car produced from 1978 to 1995.

Source: Wikipedia

## Thursday, November 17, 2011

### 1068

1068 = 22 x 3 x 89.

1068 has the representation 1068 = 210 + 44.

1068 is a divisor of 554 - 1.

NGC 1068 (also known as Messier 77) is a barred spiral galaxy about 47 million light-years away in the constellation Cetus.

## Wednesday, November 16, 2011

### 309

309 = 3 x 103.

309 is a centered hendecagonal number.

309 is the smallest number whose fifth power (3095 = 2817036000549) is pandigital (contains every digit from 0 to 9 at least once).

3093 + 3090 + 3099 is a prime, with prime digital length.

309 is 373 in base 9. It is 621 in base 7 and 261 in base 11.

309 is a telephone area code serving the state of Illinois.

Source: Number Gossip

## Tuesday, November 15, 2011

### 515

515 = 5 x 103.

515 is the number of graphs on six vertices with no isolated vertices.

515 is 20003 in base 4 and 1003 in base 8. It is 203 in base 16.

515 is the sum of nine consecutive primes: 515 = 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73.

In The Divine Comedy, Dante Alighieri wrote that the Apocalypse would be preceded by a messenger represented by the number "five hundred and ten and five" (515).

## Monday, November 14, 2011

### 904

904 = 23 x 113.

904 has a representation as a sum of two squares: 904 = 22 + 302.

904 is the maximum number of regions into which 42 lines divide the plane. It is a lazy caterer's number (central polygonal number) for 42 cuts.

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

904 is 12104 in base 5 and 4104 in base 6. It is 1214 in base 9, and it is 404 in base 15 and 323 in base 17.

The Porsche 904 was an automobile produced in 1964 and 1965.

## Friday, November 11, 2011

### 111111

111111 = 3 x 7 x 11 x 13 x 37.

111111 is a divisor of 1003 - 1.

111111 has the representation 22 x 34 x 73 - 21.

The 111,111th triangular number is palindromic: 6,172,882,716. The 1111th triangular number (617,716) and the 11th triangular number (66) are also palindromic.

111111 x 111111 = 12345654321.

1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111

3 x 37 = 111
33 x 3367 = 111111
3333 x 33336667 = 111111111111

Source: Prime Curios!

## Thursday, November 10, 2011

### 973

973 = 7 x 139.

973 is 12343 in base 5. It is 4301 in base 6, 1301 in base 9, and 301 in base 18.

973 is the sum of five positive fifth powers: 973 = 35 + 35 + 35 + 35 + 15.

973 is divisible by the sum of the squares of its digits: 92 + 72 + 32 = 139.

Mr. 973 is a hip hop performer based in New Jersey.

## Wednesday, November 9, 2011

### 567

567 = 34 x 7.

567 is the smallest possible sum of primes that are formed using all 10 digits: 567 = 401 + 89 + 67 + 5 + 3 + 2.

567 is the smallest number that together with its square (5672 = 321489) uses the digits 1 to 9 exactly once.

567 is 4232 in base 5 and 2343 in base 6. It is 700 in base 9.

567 is a divisor of 266 - 1.

The EMD 567 is a line a diesel engines produced by General Motors from 1938 until 1966 for locomotives.

## Tuesday, November 8, 2011

### 968

968 = 23 x 112.

968 is an Achilles number. Each prime factor occurs with an exponent greater than 1, but the number itself is not a perfect power.

968 has a representation as a sum of two squares: 968 = 222 + 222.

968 is a divisor of 95 - 1.

968 is 2552 in base 7 and 242 in base 21. It is 800 in base 11 and 200 in base 22.

The Porsche 968 was a sports car sold from 1992 to 1995.

## Monday, November 7, 2011

### 564

564 = 22 x 3 x 47.

564 is the largest number that can be written with all the digits from 1 to 5 (without repetition) as a sum of primes in two ways: 564 = 541 + 23 = 523 + 41.

The largest prime factor of F11 (the largest completely factored Fermat number) has 564 digits.

564 is 202220 in base 3 and 4224 in base 5. It is 1434 in base 7 and 686 in base 9. It is 345 in base 13 and 234 in base 16.

Interstate 564 (I-564), known as Admiral Taussig Boulevard, runs east for 3.03 miles, providing access to Naval Station Norfolk in Virginia.

## Friday, November 4, 2011

### 779

779 = 19 x 41.

779 is a divisor of 833 - 1.

779 is the sum of 11 consecutive primes: 779 = 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + + 89 + 97.

The sum of the digits of 779 equals the sum of the digits of the 779th prime (5927): 7 + 7 + 9 = 5 + 9 + 2 + 7 = 23.

779 yields a prime when 3 is either prefixed or appended: 3779 and 7793 are both primes.

Polaroid 779 was a high-speed color film for instant cameras.

## Thursday, November 3, 2011

### 559

559 = 13 x 43.

559 is 202201 in base 3 and 20233 in base 4.

559 is the sum of five consecutive primes and seven consecutive primes: 559 = 103 + 107 + 109 + 113 + 127 = 67 + 71 + 73 + 79 + 83 + 89 + 97.

The German submarine U-559 sank in the Mediterranean Sea in 1942, but not before British sailors managed to recover key cryptographic material from the vessel.

## Wednesday, November 2, 2011

### 643

643 is a prime number.

641 and 643 form a twin prime pair.

643 is the largest prime factor of 123456: 643(643) = 123456.

643 = (38 + 83)/(3 + 8).

A record 643 millimeters of rain fell in Sydney, Australia, in the month of June 1950.

## Tuesday, November 1, 2011

### 345

345 = 3 x 5 x 23.

345 * 2345 - 345 - 2345 is a prime number.

345 is 1333 in base 6 and 113 in base 18.

345 is the sum of three positive cubes: 345 = 73 + 13 + 13.

345 is the local telephone area code for the Cayman Islands.

## Monday, October 31, 2011

### 1393

1393 = 7 x 199.

1393 is a divisor of 923 - 1.

1393 is an NSW number.

1393 is 4030 in base 7 and 717 in base 14.

1393 is the number of nodes in a regular 16-sided polygon with all diagonals drawn.

International Brotherhood of Electrical Workers Local Union 1393 in based in Indianapolis, Indiana.

## Friday, October 28, 2011

### 768

768 = 28 x 3.

768 has a unique representation as a sum of three squares: 768 = 162 + 162 + 162.

768 is a divisor of 654 - 1.

768 is the number of subsets of {1, 2, 3, . . . , 12} that have an integer average.

416,768 = 7682 - 4162.

RSA-768 was a member of set of large semiprimes (RSA Numbers) that were part of the RSA Factoring Challenge.

## Thursday, October 27, 2011

### 273

273 = 3 x 7 x 13.

273 is 100010001 in base 2 (binary), 333 in base 9, and 111 in base 16.

The 273rd prime minus the sum of gaps between the first 273 consecutive primes minus 1 equals 273.

273 is the sum of each of two consecutive sums of consecutive numbers: 273 = 36 + 37 + 38 + 39 + 40 + 41 + 42 = 43 + 44 + 45 + 46 + 47 + 48.

The zero on the Celsius temperature is 273 (to the nearest whole number) on the Kelvin temperature scale.

## Wednesday, October 26, 2011

### 762

762 = 2 x 3 x 127.

It is a Smith number because the sum its digits is equal to the sum of the digits of its prime factors: 7 + 6 + 2 = 2 + 3 + 1 + 2 + 7 = 15.

762 is the starting location of the string 999999 in the decimal expansion of pi. This is known as the Feynman point.

762 is the sum of four consecutive primes: 762 = 181 + 191 + 193 + 197.

762 is a divisor of 193 - 1.
USS Columbus (SSN-762) was a submarine in the U.S. Navy, launched in 1992.

## Tuesday, October 25, 2011

### 540

540 = 22 x 33 x 5. All prime divisors are consecutive primes starting at 2.

540 is divisible by its reverse, 45.

540 is the sum of three distinct positive cubes: 540 = 83 + 33 + 13.

540 is the sum of the internal angles of a five-sided convex polygon (or a pentagon).

## Monday, October 24, 2011

### 1179

1179 = 32 x 131.

1179 is the sum of the squares of three consecutive primes: 1179 = 172 + 192 + 232.

1179 and 11792 (1390041) have the same digit sum: 1 + 1 + 7 + 9 = 1 + 3 + 9 + 0 + 0 + 4 + 1 = 18.

1179 is a divisor of 5310 - 1.

1179 is 2233 in base 8.

NGC 1179 is a barred spiral galaxy in the constellation Eridanus.

## Friday, October 21, 2011

### 3278

3278 = 2 x 11 x 149. The three prime factors are distinct in length.

327824 + 1 is a prime number.

The decimal expansion of pi has a string of two 7s starting in the 3278th position.

In base 6, the digits of 3278 are, in order, the first five digits of the periodic sequence with initial period 2, 3, 1, 0: 23102.

The IBM 3278 was a member of a class of video terminals (display devices) manufactured in the 1970s.

## Thursday, October 20, 2011

### 324

324 = 22 x 34.

324 is a perfect square: 324 = 182.

324 is the smallest untouchable square. Untouchable numbers are those that are not the sum of the proper divisors of any number.

324 is the largest possible product of positive integers with sum 16.

324 Bamberga, discovered in 1892, is one of the largest asteroids in the main belt.

## Wednesday, October 19, 2011

### 418

418 = 2 x 11 x 19.

418 has the property that the sum of its prime factors is equal to the product of its digits: 2 + 11 + 19 = 4 x 1 x 8 = 32.

418 is the sum of three nonzero fourth powers: 418 = 44 + 34 + 34.

418 is 262 in base 13.

418 is a telephone area code in the province of Quebec, Canada.

## Tuesday, October 18, 2011

### 924

924 = 22 x 3 x 7 x 11.

924 is the smallest value of n such that 2n choose n is divisible by n2: 1848 choose 924 is divisible by 9242.

924 is 1110011100 in base 2 (binary).

924 is a divisor of 432 - 1.

The Porsche 924 was an automobile produced from 1976 t0 1988.

## Monday, October 17, 2011

### 1136

1136 = 24 x 71.

1136 is a divisor of 1710 - 1.

1136 is a member of the toothpick sequence starting from a cross formed from four toothpicks.

1136 is the number of ways of writing 4 as a sum of eight squares.

1136 is the smallest number whose sum of squares of digits is 47: 12 + 12 + 32 + 62 = 47.

Spanish mathematician and astronomer Abraham bar Hiyya Ha-Nasi (Savasorda) died in the year 1136.

## Friday, October 14, 2011

### 613

613 is a prime number.

613 is the smallest prime such that bringing the first digit to the back produces a triangular number (136) and repeating this operation produces a square (361).

613 is the smallest number n such that the numbers of divisors of n, n + 1, n + 2, and n + 3 are k, 2k, 4k, and 8k for k = 2.

613 has a representation as a sum of two squares: 613 = 172 + 182.

613 is the hypotenuse of a primitive Pythagorean triple: 6132 = 352 + 6122.

The 613 commandments (613 Mitzvot) is a numbering of the statements and principles of law, ethics, and spiritual practice contained in the Torah (the Five Books of Moses).

## Thursday, October 13, 2011

### 1029

1029 = 3 x 73.

1029 is the smallest order for which there are 19 groups.

1029 is 4433 in base 6, 3000 in base 7, and 333 in base 18. It can be written from base 2 to base 18 using only the digits from 0 to 9.

The sum of the base 2 digits (10000000101) of 1029 equals the sum of the base 4 digits (100011) of 1029.

1029 is the sum of distinct powers of 4: 1029 = 45 + 41 + 40.

The Atari 1029 printer was one of Atari's final printers for the XL series computers in 1984.