Accuracy summation question

[rkf]

(09-06-2023 07:30 PM)lrdheat Wrote:  I calculated 2000! in home by summing from 1 to 2000 log (x), and taking 10^answer, getting 3.316274+ E5735

On the WP34S, I directly get 3.31627509245+ E5735
...

I was surprised that the Prime in home disagreed with the others in just the 6th decimal.

It´s indeed strange (altough I would say it differs in the seventh place, ...487 vs. 509). Assuming the LOGs are calculated correctly to 12 digits with values rising from 0 to about 3.3, the error of one summand should be less than +/- 5E-12
If the error in summation propagates normally, I would expect in the sum an error of ca. sqrt(2000)*(+/- 5E-12) < 2.3E-10

Taking 10^ this I get 1.00000000051, so I would nevertheless expect about 9 correct places, and not 7. :-(

Addendum: BTW I just compared with my HP50g, which gives exactly the same result of 5735.52065052 for the sum of logarithms as the prime, thus indicating the 12digits arithmetics core engine is the same.