Just what it says.

spigot is a calculating program. It supports the usual arithmetic operations, square and cube roots, trigonometric and exponential functions, and a few other special functions such as erf.

spigot differs from the average calculating program in that it is an exact real calculator. This means that it does not suffer from rounding errors; in principle, it can keep generating more and more digits of the number you asked for until it runs out of memory.

In particular, if you ask for a complex expression such as sin(sqrt(pi)), then most calculating systems would compute first pi, then sqrt(pi) and finally sin(sqrt(pi)), accumulating a rounding error at each step, so that the final result had a build-up of error and you would have to do some additional error analysis to decide how much of the output you could trust.

spigot, on the other hand, does not output any digit until it is sure that digit is correct, so if you ask for (say) 100 digits of sin(sqrt(pi)) then you can be sure they are the right 100 digits.

Mark Chu-Carroll's blog covers many subjects, including mathematics, physics and programming. In this article he describes his design of a programming language suited for an editor (think about a more readable
version of TECO's language).

In order to factor (relatively) large semi-primes (i.e. semi-primes larger than 150-bits), you should (probably) just ask YAFU (Yet Another Factoring Utility, https://github.com/DarkenCode/yafu) to try to factor the number for you in parallel using a highly-optimized number field sieve such as GGNFS (GPL General Number Field Sieve) or SIQS (Self-Initialising Quadratic Sieve). By using YAFU I was able to factor a 302-bit semi-prime in a little over half an hour , as opposed to over the course of 72 minutes using Sage’s Quadratic Sieve (QS).

Sounds like an interesting book. The blog is worth reading as well.

Jeff Miller Web Pages
Words and Symbols, for example
   Images of Mathematicians on Postage Stamps
   Earliest Known Uses of Some of the Words of Mathematics
   Earliest Uses of Various Mathematical Symbols
   Ambiguously Defined Mathematical Terms at the High School Level
   A Collection of Word Oddities and Trivia
   History of American Broadcasting

A Lego-based model of the factoring machine invented by Derrick Henry Lehmer in the 1930s.

Interesting texts about mathematical teaching, history and more (german).

Collection of articles introducing areas of mathematics.

An interesting algorithm for calculating complete elliptic integrals.