TAG: Prime Numbers
March 26, 2010–

Exciting new math features have arrived in Wolfram|Alpha! Our programmers have spent the past two months developing new capabilities in optimization, probability, number theory, and a host of other mathematical disciplines. Searching for elusive extrema? Look no further! Just feed your function(s) into Wolfram|Alpha and ask for their maxima, minima, or both. You can find global maxima and minima, optimize a function subject to constraints, or simply hunt for local extrema.

We’ve also added support for a wide variety of combinatorics and probability queries. Counting combinations and generating binomial coefficients has been simplified with syntax like 30 choose 18. Want to spend less time crunching numbers and more time practicing your poker face? You can ask directly for the probability of a full house or other common hands, as well as the probabilities of various outcomes when you play Powerball, roll two 12-sided dice, or repeat any sequence of trials with a 20% chance 4 times.

The pursuit of primes has never been so simple. Imagine yourself walking the streets of an infinite city in search of “prime real estate.” You can find the nearest one simply by requesting (for example) the prime closest to 100854; alternatively, you could scope out the entire neighborhood by asking Wolfram|Alpha to list primes between 100,000 and 101,000. Would you prefer the greatest prime number with 10 digits, or will you be satisfied with any random prime between 100,000,000 and 200,000,000? The aspiring real estate agent—er, number theoretician—can also tinker with quantities like the sum of the first hundred primes or the product of primes between 900 and 1000. If your explorations take you to the realm of the composites (the addresses of houses with “sub-prime” mortgages, perhaps), you can identify numbers with shared factors by querying Wolfram|Alpha for, say, multiples of 5, 17, 21.

Other additions have brought everything from Archimedes’ axiom to semiaxes and square pyramid syntax into our body of computable knowledge and functions. Wolfram|Alpha grows daily, so stay tuned to this blog for further updates. Better yet, apply to become a Wolfram|Alpha tester for privileged access to the newest features before they go public!