I met Vaughan Jones at the IHES (Bures sur Yvette) when he was working on the Jones polynomials.
He had made a list of braids which represented all prime knots up to ten crossings, for testing.
He gave me his list for use in my graphics program. Here the same old list is used.
Jones commented that this early list may contain errors and also that he did not always find
the shortest braid word. It seems he did not make his list public, but I view it as a piece of
mathematical history.
Since Jones' old list does indeed contain errors I let the program on this page also use the list from
Thomas A. Gittings.
I checked for a number of cases that these braid words agree with those given
in knotinfo.
Errors in Jones' list which can be detected without theory are:
Nr 166 (10_82) and Nr 201 (10_117) -- they can be represented with less than
10 crossings. And Nr 34 (8_20) and Nr 35 (8_21) differ only by a 180 degree rotation, Nr 35 is
wrong, see knotinfo. I keep using Jones' list in spite of the errors, because I am so impressed
that he made his list just as a testing ground for a theory to be developed.