29 (number)

28 29 30
Cardinal twenty-nine
Ordinal 29th
(twenty-ninth)
Factorization prime
Divisors 1, 29
Roman numeral XXIX
Binary 111012
Ternary 10023
Quaternary 1314
Quinary 1045
Senary 456
Octal 358
Duodecimal 2512
Hexadecimal 1D16
Vigesimal 1920
Base 36 T36

29 (twenty-nine) is the natural number following 28 and preceding 30.

Mathematics

It is the tenth prime number, and also the fourth primorial prime. It forms a twin prime pair with thirty-one, which is also a primorial prime. Twenty-nine is also the sixth Sophie Germain prime.[1] It is also the sum of three consecutive squares, 22 + 32 + 42. It is a Lucas prime,[2] a Pell prime,[3] and a tetranacci number.[4] It is an Eisenstein prime with no imaginary part and real part of the form 3n − 1. Since 18! + 1 is a multiple of 29 but 29 is not one more than a multiple 18, 29 is a Pillai prime.[5] 29 is also the 10th supersingular prime.[6]

None of the first 29 natural numbers have more than two different prime factors. This is the longest such consecutive sequence.

29 is the aliquot sum of the odd discrete biprimes 115 and 187 and is the base of the 29-aliquot tree.

29 is a Markov number, appearing in the solutions to x2 + y2 + z2 = 3xyz: {2, 5, 29}, {2, 29, 169}, {5, 29, 433}, {29, 169, 14701}, etc.

29 is a Perrin number, preceded in the sequence by 12, 17, 22.[7]

Since the greatest prime factor of 292 + 1 = 842 is 421, which is obviously more than 29 twice, 29 is a Størmer number.[8]

29 is the smallest positive whole number that cannot be made from the numbers {1, 2, 3, 4}, using each exactly once and using only addition, subtraction, multiplication, and division.[9]

Religion

Science and astronomy

Language and literature

Geography

Military

Music and entertainment

Sport

History

References

  1. "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  2. "Sloane's A005479 : Prime Lucas numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  3. "Sloane's A086383 : Primes found among the denominators of the continued fraction rational approximations to sqrt(2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  4. "Sloane's A000078 : Tetranacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  5. "Sloane's A063980 : Pillai primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  6. "Sloane's A002267 : The 15 supersingular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  7. "Sloane's A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  8. "Sloane's A005528 : Størmer numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  9. https://faculty.fuqua.duke.edu/~dm121/Number%20Scavenger%20Hunt%20--%20Solution
  10. Caroline Finkel, Osman's Dream. New York: Basic Books (2006): xv. "The modern Turkish alphabet has 29 letters, of which three vowels and three consonants are unfamiliar to those who do not know the language, and one consonant is pronounced differently from English."
  11. Anthony Ham, Miles Roddis & Graeme Cornwallis, Norway. New York: Lonely Planet (2005): 413. "The modern Norwegian alphabet has 29 letters: those used in English, plus the vowels æ, ø and a (which are listed at the end of the alphabet)."
  12. Stephen F. Tomajczyk, To Be a U.S. Marine. New York: Zenith Imprint (2004): 155. "Twenty-nine stumpsSlang for Twenty-nine Palms Marine Corps Air-Ground Combat Center, located in California's Mojave Desert."

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