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The Source

An interesting feature in The Book of Numbers, named due to the authors' fondness for alliterative titles. By some method not explained, they devised fourteen fractions which can be applied to create an equivalant to Eratosthenes' Sieve. It works like this:

The Method

Start with 2. Then multiply this by the first of the fruitful fractions listed below that produces an integer. Repeat. Occasionally, you will get a power of 2; the exponents of these are the primes in order.

The Fourteen Fruitful Fractions

The fractions:
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

And now, a comment

I thought this sounded quite clever, so I knocked up a fairly quick graphic calculator program to do it. I have to say, it's the slowest prime finder I have ever, ever seen. My calculator finds the first two after about a minute, a few more and it finds 5. The running value gets an over-flow before it can net 7.

Turns out that, in fact, this is the commonest example of a wider class of programs Conway calls FracTran. That is noded rather well so I suggest you check it out.

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