For me it's: 2^1 to 2^16 (I remember the 8-bit era), a hazy gap and then 2^24 (the marketing for 24 bit colour in the 90s had 16777216 plastered all over it). Then it's being uncomfortably lost up to 2^31 and 2^32, which I usually recognise when I see them (hello INT_MAX and UINT_MAX), but I don't know their digits well enough to repeat. 2^64 is similar. All others are incredibly vague or unknown.
2^23 as half of 2^24 and having a lot of 8s in it seems to have put it into the "recognisable" category for me, even if it's in that hazy gap.