Polaroid made a 20,000 speed film: Dead Link Removed; it was designed for CRT reproduction. I have no idea what its keeping properties were like, although I imagine they would be pretty bad. I also don't know what the EI is, but I suspect it would be pretty close to the rated speed as you can't really push Polaroid films the same way as you can with normal films.
This is a paper based oscillographic recording material. Kodak made the Ektaline 2000 series papers which were similarly very fast and for the same reasons I described above. They were by no means 20,000 true speed due to gaining some of their speed via reflectance from the paper support.
These products came in long rolls 5" and 10" wide for a variety of "instant" processing machines and were used in huge quantity by Cape Canaveral to record instruments during launch. They were also used by geological surveys and etc., as the papers were more reliable than the inked recorders.
IIRC, they relied on high intensity UV light for exposure and had little visible sensitivity, but my memory may be faulty on this. I know that in the 60s, I was sent from the Cape to Rochester to view the new E2000 setup that was being introduced to compete with the CEC processor which had about 1/2 the speed and sensitivity. Polaroid had no competing product at that time, but Dupont reportedly did. I never saw that product, but we did use CEC stuff until the Kodak product was in full production (CEC = Consolidated Electrodynamics Corporation).
I have a full mental history of high speed papers. AAMOF, the ISO rating of Ilford MGIV is 25 in-camera, even though the emulsion is really only about ISO 6 or so and my ISO 40 film emulsion is ISO 100 - 200 on paper. Even so, a 20,000 speed paper would be a fast emulsion, but who cares about grain and sharpness on a paper?
I did not say a high speed paper could not be done. I repeat, a 20,000 ISO true film emulsion is the highest that has been made. One of the experiments showed it to have very very poor keeping. Results are not in for the newer Gilman emulsion. In the former, you would not like the grain or sharpness, but in the latter, both are pretty good.
PE