## A Sample Macro: do-primes

A Sample Macro: do-primes

To see how this three-step process works, you'll write a macro `do-primes` that provides a looping construct similar to `DOTIMES` and `DOLIST` except that instead of iterating over integers or elements of a list, it iterates over successive prime numbers. This isn't meant to be an example of a particularly useful macro—it's just a vehicle for demonstrating the process.

First, you'll need two utility functions, one to test whether a given number is prime and another that returns the next prime number greater or equal to its argument. In both cases you can use a simple, but inefficient, brute-force approach.

```(defun primep (number) (when (> number 1) (loop for fac from 2 to (isqrt number) never (zerop (mod number fac))))) (defun next-prime (number) (loop for n from number when (primep n) return n))```

Now you can write the macro. Following the procedure outlined previously, you need at least one example of a call to the macro and the code into which it should expand. Suppose you start with the idea that you want to be able to write this:

```(do-primes (p 0 19) (format t "~d " p))```

to express a loop that executes the body once each for each prime number greater or equal to 0 and less than or equal to 19, with the variable p holding the prime number. It makes sense to model this macro on the form of the standard `DOLIST` and `DOTIMES` macros; macros that follow the pattern of existing macros are easier to understand and use than macros that introduce gratuitously novel syntax.

Without the `do-primes` macro, you could write such a loop with `DO` (and the two utility functions defined previously) like this:

```(do ((p (next-prime 0) (next-prime (1+ p)))) ((> p 19)) (format t "~d " p))```

Now you're ready to start writing the macro code that will translate from the former to the latter.

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