Now, (6!)^6 is 1.39 x 10^17 and (7!)^7 is 8.26 x 10^25. Therefore one must get at least 17 terms of 1/pi in 6th iteration and 25 places in 7th iteration.
Wolfram Alpha does not allow more places of decimal in either. 0.3183 or 2.072. Therefore I am unable to check deeply with Wolfram Alpha. Any expert programmers can try this formula and blog your comments here for accurate pi. They may write a C program for instance and let me know.
Also 41206 is a very important number. It is very nearly (163+40)^2. And 41206 x (163)^(1/2) is 526083. Also 41206/(163)^(1/2) is 3227. 526083/3227 = 163. Perhaps, 2072 is very nearly (163)x(163^(1/2)) is also important. or for that matter 72 into 73 is nearly 5260
Because of so many numbers showing closeness to Heegner number 163 ; I think this formula can be a success.
Hope you have a fine day !!
My views on this topic of fast converging pi expression is over. I will not be writing more blog post on this topic. If I get a chance, I will not rest till I get 1008 places of pi.
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