Mathematics
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:
- heptagonal number, [5] and
- square pyramidal number (the sum of the squares of the integers from 1 to 5). [6]
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
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] [lower-alpha 1]
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]