I was reading about taxicab numbers on Wikipedia at: https://en.wikipedia.org/wiki/Taxicab_number#Upper_bounds_for_taxicab_numbers
What is the probability that these upper-bound values above Ta(6) might be the actual solutions?
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2"Probability" might be a confusing word to use in this question, since the statement that the listed solution is in fact the smallest one is either true or false, but I guess you're asking for someone familiar with the problem to give their informal confidence level about this statement. – Karl Feb 24 '20 at 05:11
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1@Karl on the Wiki page, it lists "Ta(6) was announced by Uwe Hollerbach on the NMBRTHRY mailing list on March 9, 2008, following a 2003 paper by Calude et al. that gave a 99% probability that the number was actually Ta(6). Upper bounds for Ta(7) to Ta(12) were found by Christian Boyer in 2006." I'm curious if the Ta(7)+'s upper bounds are at a similar level. – Feb 24 '20 at 19:44
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Interesting! It'd be helpful to mention that in your question, since there's no standard way to interpret a mathematical statement as having a probability. I imagine in this case it's based on a randomized algorithm, so the authors are technically saying "if there were a smaller solution, there's a 99% chance that we'd have found it". – Karl Feb 27 '20 at 20:07