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Exactly. That's the vagaries of the old "DOS" partition schema.
Originally the partition table only provided room for up to four
partitions. Once that became too tight, we cludged our way out
by allowing one of those four (the so-called "extended" partition
to be subdivided into further four so-called "logical" partitions.
The old, "real" partitions came to be known henceforth as "primary"
partitions.
That's why df doesn't "see" it: no file system on it.
As for /dev/sda6: df only "sees" mounted file systems, no swap.
Thus if you want to have a more complete view of what's going on
in your disk, then yes, fdisk -l is more appropriate, as jdd wrote.
You've to aim it at the "right" disk, though, and you usually have
to be root. For a first approximation df is fine, if you know how
to interpret the (incomplete) results.
regards
- -- tomás
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