29 (number)
| ||||
---|---|---|---|---|
Cardinal | twenty-nine | |||
Ordinal | 29th (twenty-ninth) | |||
Factorization | prime | |||
Prime | 10th | |||
Divisors | 1, 29 | |||
Greek numeral | ΚΘ´ | |||
Roman numeral | XXIX | |||
Binary | 111012 | |||
Ternary | 10023 | |||
Senary | 456 | |||
Octal | 358 | |||
Duodecimal | 2512 | |||
Hexadecimal | 1D16 |
29 (twenty-nine) is the natural number following 28 and preceding 30. It is a prime number.
29 is the number of days February has on a leap year.
Mathematics
[edit]29 is the tenth prime number.
Integer properties
[edit]29 is the fifth primorial prime, like its twin prime 31.
29 is the smallest positive whole number that cannot be made from the numbers , using each digit exactly once and using only addition, subtraction, multiplication, and division.[1] None of the first twenty-nine natural numbers have more than two different prime factors (in other words, this is the longest such consecutive sequence; the first sphenic number or triprime, 30 is the product of the first three primes 2, 3, and 5). 29 is also,
- the sum of three consecutive squares, 22 + 32 + 42.
- the sixth Sophie Germain prime.[2]
- a Lucas prime,[3] a Pell prime,[4] and a tetranacci number.[5]
- an Eisenstein prime with no imaginary part and real part of the form 3n − 1.
- 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.
- a Perrin number, preceded in the sequence by 12, 17, 22.[6]
- the number of pentacubes if reflections are considered distinct.
- the tenth supersingular prime.[7]
On the other hand, 29 represents the sum of the first cluster of consecutive semiprimes with distinct prime factors (14, 15).[8] These two numbers are the only numbers whose arithmetic mean of divisors is the first perfect number and unitary perfect number, 6[9][10] (that is also the smallest semiprime with distinct factors). The pair (14, 15) is also the first floor and ceiling values in the Riemann zeta function,
15 and 290 theorems
[edit]The 15 and 290 theorems describes integer-quadratic matrices that describe all positive integers, by the set of the first fifteen integers, or equivalently, the first two-hundred and ninety integers. Alternatively, a more precise version states that an integer quadratic matrix represents all positive integers when it contains the set of twenty-nine integers between 1 and 290:[11][12]
The largest member 290 is the product between 29 and its index in the sequence of prime numbers, 10.[13] The largest member in this sequence is also the twenty-fifth even, square-free sphenic number with three distinct prime numbers as factors,[14] and the fifteenth such that is prime (where in its case, 2 + 5 + 29 + 1 = 37).[15][a]
Dimensional spaces
[edit]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.[16]
In science
[edit]- The atomic number of copper.
- Saturn requires over 29 years to orbit the Sun.
Notes
[edit]References
[edit]- ^ "Sloane's A060315". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-09-05.
- ^ "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- ^ "Sloane's A005479 : Prime Lucas numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- ^ "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.
- ^ "Sloane's A000078 : Tetranacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- ^ "Sloane's A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- ^ "Sloane's A002267 : The 15 supersingular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A001358 (Semiprimes (or biprimes): products of two primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-06-14.
- ^ Sloane, N. J. A. (ed.). "Sequence A003601 (Numbers j such that the average of the divisors of j is an integer.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-06-14.
- ^ Sloane, N. J. A. (ed.). "Sequence A102187 (Arithmetic means of divisors of arithmetic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-06-14.
- ^ Cohen, Henri (2007). "Consequences of the Hasse–Minkowski Theorem". Number Theory Volume I: Tools and Diophantine Equations. Graduate Texts in Mathematics. Vol. 239 (1st ed.). Springer. pp. 312–314. doi:10.1007/978-0-387-49923-9. ISBN 978-0-387-49922-2. OCLC 493636622. Zbl 1119.11001.
- ^ Sloane, N. J. A. (ed.). "Sequence A030051 (Numbers from the 290-theorem.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-07-19.
- ^ Sloane, N. J. A. (ed.). "Sequence A033286 (a(n) as n * prime(n).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-07-19.
- ^ Sloane, N. J. A. (ed.). "Sequence A075819 (Even squarefree numbers with exactly 3 prime factors.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-07-19.
- ^ Sloane, N. J. A. (ed.). "Sequence A291446 (Squarefree triprimes of the form p*q*r such that p + q + r + 1 is prime.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
External links
[edit]- Prime Curios! 29 from the Prime Pages