Where the ten groups come from
Divide forty by four and the answer is ten. That is the derivation in full. Convention prints a fingerprint as ten blocks of four hex characters separated by spaces, and most tools widen the gap in the middle so the ten arrive as two halves of five.
The split carries no cryptographic meaning. Strip the spaces and the fingerprint is unchanged. Put different spaces in and it is still unchanged. What you are looking at is a typographic habit borrowed from every other long identifier people have had to handle by hand.
Card numbers come in fours. Phone numbers come in twos and threes. Sort codes, account numbers, product keys and reference codes all arrive pre broken, and for the same reason. It has nothing to do with what the digits mean.
What ten groups do for a reader
Short term memory holds a small number of items at once, and an item can be a single character or a block of four, which is the whole trick. Ten blocks is a load a person can carry from one window to another. Forty loose characters is not, and people who try it lose their place somewhere around the middle every time.
Grouping also gives you coordinates. Reading with somebody else, you can say the seventh group instead of counting characters twice. Lose your place and you lose one group rather than the string. When a line wraps, it breaks between groups instead of through the middle of one.
And it makes reading aloud possible. Four characters is a mouthful you can say in one breath. That matters more than it sounds, because saying a value out loud catches the class of error that silent reading is worst at.
Where attention fails across ten groups
Watch somebody compare two fingerprints and the same shape appears almost every time. They read the first group with care. They glance at the last group. They declare a match. The eight groups in between get a sweep of the eyes and no attention at all.
That is not laziness, it is how reading works. The start and the end of any sequence are the parts that stick, and recall collapses in the middle. The problem is that anybody building a lookalike spends their effort exactly where the attention goes, because the ends of a string are the cheap part to match.
A better method costs a few seconds. Start in the middle. Compare the fifth and sixth groups first, then the fourth and seventh, and only then look at the ends. A mismatch turns up early, and if none turns up you have already covered the part nobody else checks.
Reading aloud in pairs is the other method that works. One person reads groups steadily, the other follows on their own copy and says stop at the first difference. Two people reading silently agree on a mismatch far more often than either of them would like.
The last error is believing the spaces belong to the fingerprint. They do not. Forty unbroken characters and the same value in ten groups are the same value, and a tool that accepts one accepts the other.
What changes the ten
The tool doing the printing, and very little else. Some software prints five groups of eight. Some prints the run with no spaces at all. Newer key versions produce a longer fingerprint, and a longer fingerprint groups differently, so ten is a convention attached to a length rather than a rule attached to the format.
Your own habits move it further than any tool does. Keep a trusted fingerprint somewhere you can place beside a candidate and the grouping stops mattering, because a machine does the comparison. Pasting both values into a text comparison beats every reading method on this page and takes less time than any of them.
What none of this touches is the underlying value, which is covered on the forty page, or the reason the short forms fail, which is on the eight page.
Questions people ask
Does removing the spaces break anything?
No. Spacing is presentation and tools accept a fingerprint with or without it. Keep the groups when a person has to read the value and drop them when a machine does.
Why do some tools show five groups instead of ten?
Older display conventions and newer key formats both do it. The number of groups follows the length of the fingerprint and the taste of whoever wrote the tool.
Is comparing the middle really better than comparing the start?
Yes, for two separate reasons. Attention is weakest in the middle, and matching the opening of a string is the cheapest thing a forger can do. The four character page shows how cheap.