Pat B. wrote a response to my last post on the number 867-5309. In that post I pointed out that: 8675309 is a prime. 8675309 is a twin prime (8675311 is also prime). 8675309 is the hypotenuse of a (primitive) Pythagorean triple: 86753092 = 24602602+83191412. Pat asked: What is the smallest number that would meet…

# Tag: number theory

## Freeman Dyson and a mathematical puzzle in the NY Times

On March 25 the New York Times Magazine had an article about Freeman Dyson, “The Civil Heretic.” It contains an interesting mathematical problem. At Jason, taking problems to Dyson is something of a parlor trick. A group of scientists will be sitting around the cafeteria, and one will idly wonder if there is an integer…

## A 10-adic number that is a zero divisor

A few weeks ago I wrote about p-adic numbers. I mentioned that if p is not prime, then the p-adic numbers can have zero divisors; that is, there are nonzero numbers and such that . Today Foxmaths! wrote about a 10-adic number (although not using that terminology) such that (in other words is an idempotent…

## The prime number theorem in Calculus II

I attended Shahriar Shahriari’s MAA Minicourse Beyond Formulas and Algorithms: Teaching a Conceptual/thematics Single Variable Calculus Course at the 2008 Joint Mathematics Meeting. He talked about having his calculus students derive the prime number theorem. Recall that the prime number theorem states that if is the number of primes less than or equal to ,…

## What are p-adic numbers?

I am not a number theorist, but I’ve always had a distant fascination with p-adic numbers. I have a list of “neat math topics” that I want to write about on my blog, and the p-adic numbers are on that list. So I was happy to see an interesting article about them by Andrew Rich…

## Prime number worth $100K

The Electronic Frontiers Foundation was offering a $100,000 bounty on the first Marsenne prime with over 10 million digits. A Marsenne prime is a prime number of the form . The first 10 million digit prime was discovered on August 23, 2008 by a computer at UCLA. The prime, , has 12,978,189 digits. It was discovered as part…