I was nosing around my home directory, and ran into a file with the following contents:

From The Mathematical Intelligencer, vol. 3, number 1, p. 45.

Problem is by J. H. Conway.

Problem 2.4:

**A Prime Problem for the Ambidextrous**

17/91, 78/85, 19/51, 23/38, 29/33, 77/29, 95/23, 77/19, 1/17, 11/13, 13/11, 15/14, 15/2, 55/1.

Write down 2 (with your right hand). Look at these fourteen fractions and use them to generate two sequences of natural numbers by iterating the following:

If *r* is the last number you wrote with your right hand, look for the first of the fourteen fractions which, when multiplied with *r*, gives you an integer. Write the integer down (with your right hand). If this integer is a power of 2, say 2^{l}, write down *l* (with your left hand).

- What is the left-hand sequence?
- Why?
- How long does it take to generate the first 1000 primes this way?

I’ve just spent a while working through it; I’m not done yet, but I’ve decided it’s interesting enough that there was a reason why I kept it lying around, and perhaps some of my blog readers might enjoy it.

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