Here: http://donblazys.com/on_polygonal_numbers_3.pdf you will find a most astonishing function, designated as \(B(x)*\left(1-\frac{\alpha}{\mu-2*e}\right)\), that approximates \(\varpi(x)\), which is "how many polygonal numbers of order greater than 2 there are under a given number \(x\)". This function has been referenced in the Online Encyclopedia of Integer Sequences (otherwise known as OEIS) and those references can be found here: http://www.research.att.com/~njas/s...25,27&sort=0&fmt=0&language=english&go=Search The question is, how high can \(\varpi(x)\) actually be determined before our computers either "crash", "become inaccurate", or "slow to a crawl" ? The "world record" now stands at \(x=1,100,000,000,000\). Can anyone in this forum beat that? Don.
