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