Why 13 is famous as Unlucky?

Why people tend to believe on such superstitions?

What is the effect of such superstitions?

What is so interesting about 13?

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Why 13 is famous as Unlucky?

• Alexander wanted to be a God and accordingly made a 13^th statue on the place of his capital. He died and people considered that his will to be a 13^th God (12 gods, one for each month were known) was the reason of his death. After that this number was considered as unlucky.
• According to historians, there were 13 people at Christs Last Supper and Christ was crucified on Friday 13^th. So, Friday 13^th is considered as Unlucky.
• On Friday 13^th October 1307, King Philip IV of France ordered the arrest of the Knights Templar . The Templars were charged with numerous offences. Many of the accused confessed to these charges under torture. Many stories claim that the Friday the 13^th superstition comes from the historical destruction of the Knights Templar.

Why people tend to believe on such superstitions?

Let us see some reported incidences given below:

• The Rail Gazette International carried the following report in its April 1979 issue:

  " As reported in last month, opening of Indian Railway's Hassan-Mangalore line marks completion of a construction task every bit as difficult as the Waltair-Kirandul mineral line which so severely taxed I.R.Engineers a decade ago. In the highly unstable terrain of this part of Karnataka, new solutions had to be found to a number of complex engineering problems.
  
  Not the least of the difficulties was tunnel No. 13 where 5 rock falls impeded progress for months. Even Alpine-trained Engineers were perplexed until some one came up with the simplest of solutions. The tunnel was renamed as No. 12-A and suddenly all was well."

• In a British study published in the British Medical Journal in 1993, titled " Is Friday the 13^th Bad for Your Health?", a comparison was made between the ratios of traffic volume to number of accidents on two different days i.e. Friday 6^th and Friday 13^th. It was concluded that though the traffic volume was less on Friday 13^th, the number of hospitalizations due to accidents were more. Their conclusion: "Friday 13^th is unlucky for some. The risk of hospital admission as a result of a transport accident may be increased by as much as 52 percent. Staying at home is recommended."

• The most famous example of unlucky 13 myths is the unsuccessful mission of Apollo 13 launched at 13.13 hours.There was an explosion of an oxygen tank of Apollo 13, which was on its way to moon. The explosion occurred on April 13, 1970. Apollo 13 was the only unsuccessful mission by the United States of Americas NASA program to land a mission on the moon.

Update on 13-06-2003

• Columbia Space Shuttle sent into space on 16-01-2003 (1+6+0+1+2+0+0+3 = 13) exploded during reentry and all crew members including Kalpana Chawla (The no. of letters = 13) of India died.

• UPHAAR CINEMA TRAGEDY CASE (INDIA): A fire took place at Uphaar Cinema building, Delhi (India) on friday 13^th June, 1997 resulting in the death of 59 persons and injury to about 100 persons.

Update on 13-11-2012

• The number 13 is not used on Formula 1 cars. The FIA Formula 1 World Championship entry list does not have a number 13 because it was removed after two drivers, both driving cars numbered 13, were killed in crashes. The number is generally considered to be an unlucky number.

• The Mercedes-Benz, carrying Princess Diana and Dodi Al-Fayed, had hit the 13^th pillar of Pont de l'Alma at a speed of 105 km/h, resulting in the death of the Princess of Wales and her beau, the night of 31st August, 1997.

• 1970 Bangladesh Cyclone: On Friday, 13 November, 1970, a massive storm that strike the shores of the Ganges Delta in Bangladesh devastated the densely populated delta region killing lakhs of people in the 20th century's worst disaster by cyclone.

What is the effect of such superstitions?

• Some people won't go to work on Friday the 13^th.
• Some people won't eat in restaurants on Friday the 13^th
• Some people may not like wedding on Friday the 13^th.
• Some people don't like to travel on Friday the 13^th.
• Hospital beds, operating rooms and maternity units have avoided numbering rooms with the number 13.
• Its not unusual to find auditorium and stadium seats where number 13 is missing. Even airlines and theaters avoid using the number thirteen.
• Many buildings don't have 13^th floor. Many hotels don't have a room with number 13. It is sometimes called as 12A. Because superstitious people avoid themselves to be admitted into a hotel room with the number 13 or on the 13^th floor of buildings.
• According to superstition, any one with 13 letters in their name is regarded to have Devil's luck.
• Brussels Airlines even had to change its logo after superstitious passengers complained quite strongly about the 13 dots that were used to create the letter "B" in the Brussels Airlines logo. They actually changed the logo to meet consumer needs.

It has been estimated by various sources that U.S. businesses lose millions of dollars because of canceled appointments, absenteeism, etc. on Friday, the 13^th.

What is so interesting about 13?

Leaving aside the superstitions views, let us see how fascinating the number 13 from mathematical point of view is.

• Reverse of the square of 13 is the same as the square of the reverse of 13 i.e. 13²= 169; on reversing 169, we get 961 which is the same as the square of reverse of 13 i.e. 31² = 961.

  13 x 13 = 169
  31 x 31 = 961

• Number 13 is the smallest prime number which can be expressed as the sum of the squares of two prime numbers i.e.

  13 = 2² + 3²

  Where 2, 3, 13 are prime numbers.

• From number 13 if we subtract the sum of its digits, we get a perfect square i.e.

  13 - (1 + 3) = 9 = 3²

  Also if the product of digits of 13 is added to it, we again a perfect square i.e.

  13 + (1 x 3) = 16 = 4²

• Consider the equations:

  13²= 169
  31²= 961

  If we insert the + sign between all the digits of above equation, the equation still holds good i.e.

  (1+3)² = 1+6 +9
  (3+1)² = 9 +6+1

• The smallest number whose sum of digits is 13 is a perfect square i.e. 49 = 7² and 4 + 9 = 13.
• The smallest square which contains last three digits alike is 1444. The sum of digits of this number is also 13 i.e.

  1+4+ 4+ 4 = 13

• If we place the number 13 before its reverse i.e. 31 we get the number 1331 which is a cubic number i.e. 1331= 11³
• If we take the cube of number 13 i.e. 13³ = 2197 and rearrange the digits of the cube 2197 we get the famous Ramanujan's number 1729.
• 13 is the average number of the prime factors of the famous Ramanujan's number 1729. i.e.

  1729 = 7 x 13 x 19

  (7 + 13 + 19) ÷ 3 =13

• Take the square of the number 13 i.e. 13² = 169. Now we see that 169 contains many perfect squares in it:
  
  The sum of the digits of the number 169 is a perfect squares and is the square of the sum of the digits of the original number i.e.

  1+6+9 = 16 = 4² =(1+3)²

  Divide the number in two blocks i.e. 16 and 9. We see that both are perfect square numbers and their sum and product is a perfect square:

  16 + 9 = 25 = 5²
  16 x 9 = 144 = 12²

  The number 169 which is perfect square can be expressed as sum of two square i.e.

  169 = 13² = 5² + 12²

  The number 169 can be expressed by number of its two block i.e. 16 and 9 which are perfect squares as follows:

  169 = (16 + 9) + (16 x 9)

• Sum of the numbers from 1 to 13 gives 91 which is the smallest number which can be expressed as the sum of two cubes and also as the difference of two cubes i.e.

  91 = 3³ + 4³
  91 = 6³ - 5³

• 13 is the only integer which along with its fourth power can be expressed as the sum of two consecutive squares i.e.

  13 = 2² + 3²
  13⁴ = 120² + 121²

• The reciprocal of number 13 gives

  1/13 = 0.076923076923076923...

  i.e. the number 076923 repeating indefinitely. This number 76923 is one of the most curious numbers in mathematics.On multiplying the number 76923 by successive multiples of 13, the following beautiful pattern is obtained.

  76923	x	13	=	0999999
  76923	x	26	=	1999998
  76923	x	39	=	2999997
  76923	x	52	=	3999996
  76923	x	65	=	4999995
  76923	x	78	=	5999994
  76923	x	91	=	6999993
  76923	x	104	=	7999992
  76923	x	117	=	8999991
  76923	x	130	=	9999990

  I published the above properties in reference [1] and [2]. Some more fascinating Prime Curios about 13 can be found at PRIME CURIOS.

Some New Fascinating Properties

• The Sum of all Prime Numbers up to 13 is equal to the 13^th Prime Number and this is the largest such number.
• The number 13 is a Fibonacci prime, so also the 13^th Fibonacci number is Fibonacci Prime and this is also the largest known such number.
• The sum of first 13 Prime numbers is 238, whose sum of digits is 13.

  Update on 1-12-2002

• The number 13 appears for the first time at 111^th place in decimal expansion of Pi as shown below:

  3.141592653589793238462643383279502884197169399375105820974944
     592307816406286208998628034825342117067982148086513282306647
     093844609550582231725359408128481117450284102701938521105559
     6446229489549303820......

  Interestingly sum of digits of prime factors of 111 ( i.e. 3*37) is 13.

• The concatenation of cubes of numbers from 13 to 1 i.e.

  2197172813311000729512343216125642781  is prime.

• The only known prime in the Smarandache Mirror sequence i.e.
  

  1, 212, 32123, 4321234, 543212345, 65432123456, 7654321234567,
  876543212345678, 98765432123456789,109876543212345678910,
  1110987654321234567891011, 12111098765432123456789101112,
  131211109876543212345678910111213,
  1413121110987654321234567891011121314,.....
  is the 13^thterm in the sequence.

• A beautiful anagrammatical equation involving 13 is:

  ELEVEN + TWO = TWELVE + ONE.

• The Smallest composite titanic number whose none of the prime factor is known is 10⁹⁹⁹ + 13.

  Update on 13-06-2003

• 13 is the Smallest Prime which can be represented as sum of two composite numbers and also sum of two prime numbers in only one way.

Update on 01-01-2004

• Sum of digits of Smallest 13 digit Prime (i.e. 1000000000039) is equal to 13.
• 31^st Prime is preceded by 13 consecutive composite numbers.

Some interesting facts

• The premier of many countries is designated as PRIME MINISTER containing exactly 13 letters.
• Some other common designations containing 13 letters are CHIEF MINISTER, CHIEF ENGINEER, VICE PRINCIPAL etc.
• Some of the mathematical terms containing 13 letters are PERPENDICULAR, CIRCUMFERENCE, ANTILOGARITHM, APPROXIMATION, QUADRILATERAL and INDETERMINATE.
• The standard length of Broad Gauge Rail in India is 13 meters.
• Teen-hood starts from Thirteen.
• 13 is also called a moon number because the moon moves approx. 13 degrees a day so there are 13 moon months in a year.

  Update on 1-12-2002

• In Japan, the numbers 4 and 9 are considered unlucky, not because 13 can be represented as sum of these two perfect squares but because of their pronunciation. In Japanese, four is pronounced as shi which is the same pronunciation as death. Nine is pronounced ku which has the same pronunciation as torture.
• There is always atleast one friday 13^th in each year. In some years, there are two and rarely three. Most recently in 2015 there were three friday 13^th. which occured in Feb, March and November. Next such year when there will be three friday 13^th is 2026.

Update on 01-01-2004

• SADDAM HUSSEIN contain 13 letters (S,A,D,D,A,M,H,U,S,S,E,I,N) and was captured on 13 ^th December, 2003.

Update on 13-11-2012

• There are 13 major joints in our body which give us the power of physical activity (1 neck, 2 shoulder, 2 elbows, 2 wrists, 2 hips, 2 knees and 2 ankles).
• Friday the 13^th computer virus infected hundreds of personal computers across the UK on 13 January, 1989, wiping out program files at a time when computer viruses were a relatively new threat.
• Microsoft has skipped the Number 13: Microsoft went from Office 2007 (version 12) directly to office 2010 (version 14), skipping version 13, the number that Microsoft assumes may be not so lucky.
• There are 13 cards of each suit in a deck of playing cards.
• Thirteen has special importance in the United States because it was founded with the thirteen original colonies. The original flag had thirteen stars, one for each state. New stars have since been added whenever a new state joins the union. The American flag has thirteen horizontal stripes.
  The Great Seal of the United States both sides of which can be seen on the back of a U.S. one-dollar bill, contain 13 stars above the Eagle, 13 Stripes on the Seal's emblem, 13 leaves on the olive branch, 13 olives, 13 arrows, 13 layers of bricks (steps) in the truncated pyramid.

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[1] Unlucky Thirteen, Shyam Sunder Gupta, INDIAN RAILWAYS, December 1985, India
[2] Fascinating properties of number 13, Shyam Sunder Gupta, SCIENCE REPORTER, May 1986, India
[3] Fascinating Unlucky 13, Shyam Sunder Gupta, INDIAN RAILWAYS, September 2012, India

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