# 55

This number is a composite.

55 is 5 times the 5th prime. [Woods]

Every number greater than 55 is the sum of distinct primes of the form 4n + 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 50 55 52 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
```