Inspired by NUMBERWORLD page, I have done some computations of irrational constants with challenging accuracy.
So far (due to required space) I cannot publish full results, but only summaries for reference. I will publish full results soon.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Newton algorithm was used with own routines written with C and MPFR library. Accuracy was compared with current world record computation of square root of 2 and golden ratio constant.
Verification was done in typical way - after reaching desired precision, the result was powered to appropriate power to prove that difference is beyond this accuracy.
In each case, to be sure about correctness of ending digits, 50 more digits were computed then truncated.
Computed during long nigths of December 2013 🙂
...of numbers up to 100. 2-11 with 10,000,000,000 digits accuracy, others with 2,500,000,000 accuracy.
...of numbers up to 100. 2-10 with 10,000,000,000 digits accuracy, others with 1,000,000,000 accuracy.
...with 20,000,000,000 digits accuracy.
...with 10,000,000,000 digits accuracy. Solutions of x^n - x - 1 = 0 polynomial, for n in range from 2 to 10. For n = 2 it is equal to "golden ratio" (phi constant), for n = 3 it is called simply "plastic number".