Cycle of New Year’s Days

Stegonography attempts to prevent messages from being read by unintended recipients by hiding the messages rather than (or in addition to) encrypting them. Stegonography is used when you not only want to keep your communication private, you want to hide the fact that you’ve communicated at all. Fun fact: The words stegonography and stegosaurus...

A blog carnival is a way to discover new blogs. Writers on a given topic, such as math, take turns hosting the carnival, featuring recent posts from various writers. Blog carnivals were once much more common, but most have faded away. The Carnival of Mathematics, however, is one of the oldest carnivals and still active, […] The post Carnival of...

The previous post showed that there are 10 Abelian groups that have 2025 elements. Implicitly that means there are 10 Abelian groups up to isomorphism, i.e. groups that are not in some sense “the same” even if they look different. Sometimes it is clear what we mean by “the same” and there’s no need to […] The post Up to isomorphism first appeared...

Every finite Abelian group can be written as the direct sum of cyclic groups of prime power order. To find the number of Abelian groups of order 2025 we have to find the number of ways to partition the factors of 2025 into prime powers. Now 2025 = 34 × 52. We can partition 34 […] The post Abelian groups of order 2025 first appeared on John D. Cook.

RSA public key cryptography begins by finding a couple large primes. You essentially do this by testing random numbers until you find primes, but not quite. Filippo Valsorda just posted a good article on this. Suppose you’re looking for a 1024-bit prime number. You generate random 1024-bit numbers and then test until you find one […] The post...