As an undergraduate, my psychology tutor dryly commented to me that the best way to get a paper widely read was to give it a memorable title, like “the magic number 7, plus or minus 2”.

Miller, G. A. (1956). The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychological Review, 63(2), 81–97.
https://doi.org/10.1037/h0043158

Here is the abstract, in full:

A variety of researches are examined from the standpoint of information theory. It is shown that the unaided observer is severely limited in terms of the amount of information he can receive, process, and remember. However, it is shown that by the use of various techniques, e.g., use of several stimulus dimensions, recoding, and various mnemonic devices, this informational bottleneck can be broken. 20 references.

Out of respect for George Miller, this post will be equally brief. His paper became a classic because it showed that we perceive the world through an attentional bottleneck, one which we would like to expand, but which has not proved possible despite every training effort over the last 63 years, other than for a few heroic individuals who practiced digit span hard for months, and then find their abilities did not generalize to other memory tasks. Like in a funnel, the many possible inputs of experience must slowly swirl down a narrow spout into the waiting brain. A grievous restriction.

All is not lost, because we can cope with our restricted scope by learning how to “chunk” data into other more meaningful units. So, although we are cabined, cribbed, confined in actuality, we have found heuristics to cope with our limitations. Despite that, people still yearn to achieve even more if they could increase their span just a little.

The much-vaunted Flynn effect has done nothing for digit span, although it may have increased the easy “digits forwards” performance just a fraction, at the cost of reducing the harder and more predictive “digits backwards” performance by a similar fraction, resulting in no change overall.

http://www.unz.com/jthompson/working-memory-bombshell/

How do other species fare in this regard? In a very brief review, Manoochehri (2019) lays out the basic picture and wonders how memory span evolved.

The evolution of memory span: a review of the existing evidence. Majid Manoochehri

https://psyarxiv.com/zdsya/

The existing evidence shows that chimpanzees have a memory span of about 5 items (Inoue &Matsuzawa, 2007; Kawai & Matsuzawa, 2000).

Lately, Toyoshima et al. (2018) have stipulated that rats are able to remember 5 objects at once.

Baboons reveal a memory span of about 4 to 5 items (Fagot & DeLillo, 2011).

Herman etal. (2013) have suggested a memory span of about 4 to 5 items for bottlenose dolphins.

The results of studying two rhesus monkeys Swartz et al. (1991) suggest a memory span of about 4 objects.

Similar work by Sugita et al. (2015) has argued that rats’ memory span is approximately 4 items.

Terrace (1993) has found it takes a pigeon 3-4 months to learn a 4-item list, which suggests that 4 is a pigeon’s memory span.

More studies of more animals would be needed to show if the jump from 4-5 items up to the human 7 items is the massive discontinuity it appears to be. Did we pick up a mutation 60 to 130 thousand years ago which gave us the bandwidth to use grammatical computations, greater articulatory rehearsal, leading to automatic long-term storage, and the beginnings of introspection, self-reflection, consciousness and symbolic thought? It might even have given us the ability to create and enjoy music, a language-like spin off from newly acquired processing skills.