# Plan9: generate primes

Published:

`Plan9 primes`

generates all the primes in a specified range. It uses wheel factorization with a bit array. You can find the code on GitHub (local cache).

# The wheel

Wheel factorization is done with the primes `2`

, `3`

, `5`

and `7`

. The `wheel`

array is prefilled with the gaps between the spokes modulo \(2*3*5*7=210\). The table can be generated with (wheel.go):

```
package main
import (
"fmt"
)
func main() {
primes := []int{2, 3, 5, 7}
N := 1
for _, p := range primes {
N *= p
}
prev := 1
for i := 3; i <= N; i += 2 {
ok := true
for _, p := range primes {
if i%p == 0 {
ok = false
break
}
}
if ok {
fmt.Printf("%d ", i-prev)
prev = i
}
}
}
```

Run it with:

```
$ go run wheel.go
10 2 4 2 4 6 2 6 4 2 4 6 6 2 6 4 2 6 4 6 8 4 2 4 2 4 8 6 4 6 2 4 6 2 6 6 4 2 4 6 2 6 4 2 4 2 10
```

An interesting optimization is that we don't check a candidate prime against each spoke, but we `mark`

all the multiplies of the spokes as composites within `table`

(which is a bitarray). This is called wheel sieve.

# The bitarray

Commonly one sees a bitarray implemented as (bitarray.c):

```
void
bitset(unsigned char *a, unsigned int i) {
a[i>>3] |= 1 << i&7;
}
int
bitget(unsigned char *a, unsigned int i) {
return a[i>>3] & (1 << i&7);
}
```

`Plan9 primes`

instead of shifting, indexes inside `bittab`

.

# See also

- Prichard's wheel sieve on Programming Praxis
- man modf