# 55

This number is a composite.

55 is 5 times the 5^{th} prime. [Woods]

Every number greater than 55 is the sum of distinct primes of the
form 4*n* + 3. [Wells]

If sigma(*n*)/*n* is greater than 9, then *n* has
at least 55 distinct prime factors. [Laatsch]

Klimov (1975) showed that all integers are the sum of at most 55 prime numbers.

The number of circular primes below 1,000,000. [Mudder]

The smallest semiprime of the form (4n + 3)*(4n - 3). [Bajpai]

2^55-55 is the largest non-titanic prime of form 2^n-n, where n is a composite number. [Loungrides]

π(55) = 5+5+5+5/5 which requires 5 "5s" on the right. [Worrom]

A solution to the "Prime Queen Attacking Problem" including a configuration of maximal primes attacked for a Bishop (7 on one diagonal and 6 on the other). Found by Alessandro Casini of Italy in September 2023:

11 14 39 60 09 64 07 62 38 41 10 13 54 61 58 01 15 12 53 40 59 08 63 06 42 37 505552 05 02 57 49 16 43 36 29 56 25 04 44 19 46 51 24 03 30 33 17 48 21 28 35 32 23 26 20 45 18 47 22 27 34 31