29 (number)

Last updated
28 29 30
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.

Contents

29 is the number of days February has on a leap year.

Mathematics

29 is the tenth prime number.

Integer properties

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,

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 of imaginary parts of non-trivial zeroes in the Riemann zeta function,

29 is the largest prime factor of the smallest number with an abundancy index of 3,

1018976683725 = 33 × 52 × 72 × 11 × 13 × 17 × 19 × 23 × 29 (sequence A047802 in the OEIS )

It is also the largest prime factor of the smallest abundant number not divisible by the first even (of only one) and odd primes, 5391411025 = 52 × 7 × 11 × 13 × 17 × 19 × 23 × 29. [11] Both of these numbers are divisible by consecutive prime numbers ending in 29.

15 and 290 theorems

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: [12] [13]

The largest member 290 is the product between 29 and its index in the sequence of prime numbers, 10. [14] The largest member in this sequence is also the twenty-fifth even, square-free sphenic number with three distinct prime numbers as factors, [15] and the fifteenth such that is prime (where in its case, 2 + 5 + 29 + 1 = 37). [16] [lower-alpha 1]

Dimensional spaces

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. [18]

In science

In religion

Notes

  1. In this sequence, 29 is the seventeenth indexed member, where the sum of the largest two members (203, 290) is . Furthermore, 290 is the sum of the squares of divisors of 17, or 289 + 1. [17]

Related Research Articles

10 (ten) is the even natural number following 9 and preceding 11. Ten is the base of the decimal numeral system, the most common system of denoting numbers in both spoken and written language.

21 (twenty-one) is the natural number following 20 and preceding 22.

In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime numbers, there are also infinitely many semiprimes. Semiprimes are also called biprimes, since they include two primes, or second numbers, by analogy with how "prime" means "first".

34 (thirty-four) is the natural number following 33 and preceding 35.

57 (fifty-seven) is the natural number following 56 and preceding 58.

58 (fifty-eight) is the natural number following 57 and preceding 59.

92 (ninety-two) is the natural number following 91 and preceding 93.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

300 is the natural number following 299 and preceding 301.

400 is the natural number following 399 and preceding 401.

127 is the natural number following 126 and preceding 128. It is also a prime number.

138 is the natural number following 137 and preceding 139.

777 is the natural number following 776 and preceding 778. The number 777 is significant in numerous religious and political contexts.

216 is the natural number following 215 and preceding 217. It is a cube, and is often called Plato's number, although it is not certain that this is the number intended by Plato.

168 is the natural number following 167 and preceding 169.

177 is the natural number following 176 and preceding 178.

744 is the natural number following 743 and preceding 745.

30,000 is the natural number that comes after 29,999 and before 30,001.

1234 is the natural number following 1233, and preceding 1235.

References

  1. "Sloane's A060315". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-09-05.
  2. "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  3. "Sloane's A005479 : Prime Lucas numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  4. "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.
  5. "Sloane's A000078 : Tetranacci numbers". 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 A002267 : The 15 supersingular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  8. Sloane, N. J. A. (ed.). "SequenceA001358(Semiprimes (or biprimes): products of two primes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-06-14.
  9. Sloane, N. J. A. (ed.). "SequenceA003601(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.
  10. Sloane, N. J. A. (ed.). "SequenceA102187(Arithmetic means of divisors of arithmetic numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-06-14.
  11. Sloane, N. J. A. (ed.). "SequenceA047802(Least odd number k such that sigma(k)/k is greater than or equal to n.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-07-26.
  12. 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.
  13. Sloane, N. J. A. (ed.). "SequenceA030051(Numbers from the 290-theorem.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-07-19.
  14. Sloane, N. J. A. (ed.). "SequenceA033286(a(n) as n * prime(n).)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-07-19.
  15. Sloane, N. J. A. (ed.). "SequenceA075819(Even squarefree numbers with exactly 3 prime factors.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-07-19.
  16. Sloane, N. J. A. (ed.). "SequenceA291446(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.
  17. Sloane, N. J. A. (ed.). "SequenceA001157(a(n) as sigma_2(n): sum of squares of divisors of n.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-07-21.
  18. 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.