# 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.