I'm currently testing a few non-15k's of extremely low Nash weight up to 1M. You may have noticed the prime 243163663*2^919087-1 I have found recently. For the k's I'm testing usually only about 400-500 n's survive the sieve and need to be tested by LLR. So this could be done on a typical machine in about one month or so. But the chances of finding a prime is at least very low. Nevertheless, if you find one it will be a big one

Until now I've computed Nash weights for all k<350.000.000 and there are a lot of interesting candidates, e.g. almost about 50.000 candidates have a Nash weight less than 100. For my tests I've picked only those with weights lower than 20. If you're interested in a list of possible candidates, e.g. the "less than 100 list", just leave a note here in the forum.

Thomas L8 L19 L10