55 (fifty-five) is the natural number following 54 and preceding 56.
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).
The prime indices in the prime factorization of 55 = 5 × × --> 11 {\displaystyle 55=5\times 11} are the respectively the third and fifth, where the first two Fermat primes of the form 2 2 n + 1 {\displaystyle 2^{2^{n}}+1} are 3 {\displaystyle 3} and 5 {\displaystyle 5} [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 7 − − --> 2 = 5 {\displaystyle 7-2=5} , 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]
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