55 (number)

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← 54 55 56 →
Cardinalfifty-five
Ordinal55th
(fifty-fifth)
Factorization5 × 11
Divisors1, 5, 11, 55
Greek numeralΝΕ´
Roman numeralLV
Binary1101112
Ternary20013
Senary1316
Octal678
Duodecimal4712
Hexadecimal3716

55 (fifty-five) is the natural number following 54 and preceding 56.

Mathematics[edit]

55 is the fifteenth discrete semiprime,[1] and the second with 5 as the lowest non-unitary factor. Thus, of the form 5 × q with q a higher prime, in this case equal to 11.

It contains an aliquot sum of 17; the seventh prime number, within an aliquot sequence of one composite number (55, 17, 1, 0) that is rooted in the 17-aliquot tree.

55 is the tenth Fibonacci number.[2] It is the largest Fibonacci number to also be a triangular number (the tenth as well);[3] it is furthermore the fourth doubly triangular number.[4]

55 is also an early member inside other families of polygonal numbers; it is strictly (when including 0 as the zeroth indexed member) the fifth:

It is also the fourth centered nonagonal number,[7] and the third centered icosahedral number.[8]

In decimal, 55 is a Kaprekar number,[9] whose digit sum is also 10. It is the first number to be a sum of more than one pair of numbers which mirror each other (23 + 32 and 14 + 41).

Fermat primes[edit]

The prime indices in the prime factorization of are the respectively the third and fifth, where the first two Fermat primes of the form are and [10] (11 is also the third super-prime).

Where 17 — the aliquot part of 55 — is the third Fermat prime, the fifty-fifth prime number 257[11] is the fourth such prime number.[10] The base-ten digit representation of the latter satisfies a subtractive concatenation of , wherein 77 is the fifty-fifth composite number.[12][a]

In decimal representation, the fifth and largest known Fermat prime is 65537,[10] which contains a "55" string inside (and where as a number, 637 is the eleventh non-trivial decagonal number).[13]

Science[edit]

Astronomy[edit]

Music[edit]

Transportation[edit]

  • In the United States, the National Maximum Speed Law prohibited speed limits higher than 55 miles per hour (90 km/h) from 1974 to 1987

Film[edit]

Years[edit]

Other uses[edit]

See also[edit]

References[edit]

  1. ^ 77 is the twenty-second discrete (square-free) semiprime, and 55 is the fifteenth, where 15 is equivalent to the product of 3 × 5, and as such the fourth discrete semiprime.[1]
  1. ^ a b Sloane, N. J. A. (ed.). "Sequence A006881 (Squarefree semiprimes: Numbers that are the product of two distinct primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-04.
  2. ^ "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers: a(n) is the binomial(n+1,2): n*(n+1)/2 equal to 0 + 1 + 2 + ... + n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-06.
  4. ^ "Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  5. ^ "Sloane's A000566 : Heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  6. ^ "Sloane's A000330 : Square pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  7. ^ "Sloane's A060544 : Centered 9-gonal (also known as nonagonal or enneagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  8. ^ Sloane, N. J. A. (ed.). "Sequence A005902 (Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence for f.c.c. lattice.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-12-29.
  9. ^ "Sloane's A006886 : Kaprekar numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  10. ^ a b c Sloane, N. J. A. (ed.). "Sequence A000215 (Fermat numbers: a(n) equal to 2^(2^n) + 1.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-04.
  11. ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-12-09.
  12. ^ Sloane, N. J. A. (ed.). "Sequence A002808 (The composite numbers: numbers n of the form x*y for x > 1 and y > 1.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-12-09.
  13. ^ Sloane, N. J. A. (ed.). "Sequence A001107 (10-gonal (or decagonal) numbers: a(n) equal to n*(4*n-3).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-12-09.