← 28 29 30 →
Cardinaltwenty-nine
Ordinal29th
(twenty-ninth)
Factorizationprime
Prime10th
Divisors1, 29
Greek numeralΚΘ´
Roman numeralXXIX
Binary111012
Ternary10023
Senary456
Octal358
Duodecimal2512

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

## Mathematics

• 29 is the tenth prime number, and the fifth primorial prime.
• 29 forms a twin prime pair with thirty-one, which is also a primorial prime. Twenty-nine is also the sixth Sophie Germain prime.[1]
• 29 is the sum of three consecutive squares, 22 + 32 + 42.
• 29 is a Lucas prime,[2] a Pell prime,[3] and a tetranacci number.[4]
• 29 is an Eisenstein prime with no imaginary part and real part of the form 3n − 1. 29 is also the 10th supersingular prime.[5]
• None of the first 29 natural numbers have more than two different prime factors. This is the longest such consecutive sequence.
• 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.[6]
• 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.[7]
• 29 is the number of pentacubes if reflections are considered distinct.

The 29th dimension is the highest dimension for compact hyperbolic Coxeter polytopes that are bounded by a fundamental polyhedron, and the highest dimension that holds arithmetic discrete groups of reflections with noncompact unbounded fundamental polyhedra.[8]

## 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. ^ "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 A002267 : The 15 supersingular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
6. ^ "Sloane's A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
7. ^ "Sloane's A060315". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-09-05.
8. ^ Vinberg, E.B. (1981). "Absence of crystallographic groups of reflections in Lobachevskii spaces of large dimension". Functional Analysis and Its Applications. 15 (2). Springer: 128–130. doi:10.1007/BF01082285. eISSN 1573-8485. MR 0774946. S2CID 122063142.
9. ^ 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."
10. ^ Mäkinen, Panu. "Finnish Grammar - Alphabet". users.jyu.fi. Retrieved 21 March 2018.
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 å (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 stumps—Slang for Twenty-nine Palms Marine Corps Air-Ground Combat Center, located in California's Mojave Desert."