My wife and I are distantly related 4C2R/6C2R from a shared ancestor born in 1751 (about 4 cM from GEDMatch). My wife being descended from his daughter. We have yet to find any matches that match both of us but she has a number of matches descended from the aforementioned daughter and I have one!
As long as you are 100% certain about that from the paper trail. A match length of 4cM has a substantially higher probability of being false (identical by chance etc.) than a genuine match.
Unfortunately, I don't think you can rely on a single 4cM match length between two individuals as proof of anything.
I have just repeated an experiment I did some time ago, almost certainly with different people, as I have no way of remembering the identities of the ones I chose previously.
Search online for GEDmatch kit numbers at random, for people that you have never heard of and have no known connection to. The first one that I found just now was to a woman in Galway. I then did an Autosomal One to One comparison between my kit and hers on GEDmatch, having set the included minimum segment length to 3cM. We share 7 segments at between 3.0 and 3.9 cM, and one at 5.4 cM.
The second one I found at random was to a man in Italy. A One to One comparison with the same settings reports that we share 10 segments between 3.0 and 4.7cM.
Third attempt was with another male randomly picked from a google search, who lives in Philadelphia. 9 shared segments between 3.0 and 4.7cM again.
I have no known connections to Ireland, Italy or Philadelphia in my direct lines of descent, have never heard of the three people I chose, nor do I recognise their surnames. I just found them randomly via Google by searching for GEDmatch kit numbers.
Another that I had saved; a man with the same surname as my paternal grandmother, and who claims to be descended from my 6X GGF in Somerset. He was of interest because his tree goes back to a family in Shepton Mallet, where he asserts that my GX6 GGF was born, whereas all my research indicates that he was born in a small village still in Somerset, but some distance away, to a family who had lived in that village since at least the 15th century, although I don't have a direct and proven line back that far! But nothing in my family back to c. 1700 indicates any link to a direct ancestor in or from Shepton Mallet. Nevertheless there are a lot of families with the same surname all over Somerset. We share 6 segments between 3.0 and 4.6cM.
Whilst we could be related even further back, my conclusion is that our "match" is just random noise, and no evidence of anything. That is why most testing companies set their minimum match lengths to around 6-7cM for showing matches, including the default setting for the One to One Comparison tool on GEDmatch. Even at that level, the probability is that up to half of them are likely to be false matches.
I did read somewhere that if you set the minimum match length at 3cM, you are more likely than not to find at least one matching segment to virtually any other person on the planet, via autosomal matching, purely as a result of chance rather than any genuine relationship.
