Number Gossip
(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)
Unique Properties of 38
- 38 is the magic constant in the only possible magic hexagon (which utilizes all the natural integers up to and including 19)
- XXXVIII (=38) is lexicographically the last string which represents a valid Roman numeral
- 38 is the largest even number which cannot be written as the sum of two odd composite numbers
- 38 is the largest known even number which can be represented as a sum of two distinct primes in only one way (38 = 31 + 7)
- 38 is the sum of squares of the first three primes (2^2 + 3^2 + 5^2)
Common Properties of 38
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime numbers.
The number n is deficient if the sum of all its positive divisors except itself is less than n.
Compare with perfect and abundant numbers.
A number is even if it is divisible by 2.
Numbers that are not even are odd. Compare with another pair -- evil and odious numbers.
The number n is odious if it has an odd number of 1's in its binary expansion.
Guess what evil numbers are.
A number is said to be square-free if its prime decomposition contains no repeated factors.
The next Ulam number is uniquely the sum of two earlier distinct Ulam numbers.