# 29 (number)

 ← 28 29 30 →
Cardinaltwenty-nine
Ordinal29th
(twenty-ninth)
Factorizationprime
Divisors1, 29
Roman numeralXXIX
Binary111012
Ternary10023
Quaternary1314
Quinary1045
Senary456
Octal358
Duodecimal2512
Vigesimal1920
Base 36T36

 ← 28 29 30 →
Cardinaltwenty-nine
Ordinal29th
(twenty-ninth)
Factorizationprime
Divisors1, 29
Roman numeralXXIX
Binary111012
Ternary10023
Quaternary1314
Quinary1045
Senary456
Octal358
Duodecimal2512
Vigesimal1920
Base 36T36

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. It is also the sum of three consecutive squares, 22 + 32 + 42. It is a Lucas prime, a Pell prime, and a tetranacci number. 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. 29 is also the 10th supersingular prime.

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 $x^2 + y^2 + z^2 = 3xyz$: {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.

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

## Religion

• The Bishnois community follows 29 principles. Guru Jambheshwar had laid down 29 principles to be followed by the sect in 1485 A.D. In Hindi, Bish means 20 and noi means 9; thus, Bishnoi translates as Twenty-niners.
• The number of suras in the Qur'an that begin with muqatta'at

## References

1. ^ 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."
2. ^ [1]
3. ^ 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)."
4. ^ Stephen F. Tomajczyk, To Be a U.S. Marine. New York: Zenith Imprint (2004): 155. "Twenty-nine stumps—Slang for Twenty-nine Palms Marine Corps Air-Ground Combat Center, located in California's Mojave Desert."