odditudes-and-weirdities

Happy Prime Numbers Day! Prime numbers are quite possibly the favorite set of numbers in mathematics. They consist of natural numbers greater than 1 that are not a product of 2 or more smaller natural numbers. The table below shows the prime numbers less than 51. Interest in prime numbers goes back to ancient times. It's long been proven that there are an infinite number of prime numbers, for example. It's long been controversial whether the number 1 should be included in the primes. Though my initial instincts would be to include it, there are reasons to exclude it . If you want to pick a fight with a mathematician, refer to prime numbers in the past tense . We celebrate prime numbers today because the date can be represented as 11/13, the largest consecutive prime numbers that represent a valid date.  

Happy Semiprime Numbers Day! Semiprime numbers are the product of exactly 2 prime numbers , so 4 (2 X 2) and 6 (2 X 3) are semiprimes, but 8 (2 X 2 X 2) and 30 (2 X 3 X 5) are not. More examples are here: Public key cryptography depends on the difficulty of factoring very large semiprime numbers for its effectiveness. Semiprime Numbers Day is celebrated on the date 10/14, or October 14, since 10 and 14 are the largest consecutive semiprime numbers forming a valid date.

Happy Composite Numbers Day! Composite numbers are sort of like the complement of the prime numbers (ignoring 1, which is neither), and each of them can be expressed as two or more prime numbers. For example, 12 = 2 X 2 X 3 (2 and 3 are primes) so it is composite, and 35 = 5 X 7 (5 and 7 are primes) so it is composite. Every positive integer greater than 1 is going to be either a prime number or a composite number. A subset of the composite numbers, the semiprime numbers , are the driving force behind  public key cryptography  Other interesting subsets of the composite numbers are the sphenic numbers and the powerful numbers . December 14 was chosen for Composite Numbers Day since they are the largest consecutive composite numbers to form a date: 12/14.