wPrime 2.0	Source: WPrime

wPrime uses a recursive call of Newton's method for estimating functions, with f(x)=x²-k, where k is the number we're sqrting, until Sgn(f(x)/f'(x)) does not equal that of the previous iteration, starting with an estimation of k/2. It then uses an iterative calling of the estimation method a set amount of times to increase the accuracy of the results. It then confirms that n(k)²=k to ensure the calculation was correct. It repeats this for all numbers from 1 to the requested maximum.

Lower calculation times are better. wPrime is multi-threaded.

wPrime 2.0 - Windows Vista 32 Million Digits (1 thread): (sec) Ranking Intel Core i7 920 51.156 Intel Core 2 Duo E8500 50.466 Intel Core 2 Duo E8400 53.64 AMD Phenom II X4 965 Black Edition 42.808 AMD Phenom II X4 955 Black Edition 45.115 AMD Phenom II X3 720 Black Edition (DDR2) 52.354 AMD Phenom II X3 720 Black Edition (DDR3) 51.901 AMD Phenom II X2 550 Black Edition 48.173 AMD Athlon II X4 620 55.083 AMD Athlon II X2 250 49.827 32 Million Digits (2 thread): (sec) Ranking Intel Core i7 920 25.828 Intel Core 2 Duo E8500 25.49 Intel Core 2 Duo E8400 27.078 AMD Phenom II X4 965 Black Edition 21.656 AMD Phenom II X4 955 Black Edition 22.682 AMD Phenom II X3 720 Black Edition (DDR2) 26.537 AMD Phenom II X3 720 Black Edition (DDR3) 26.256 AMD Phenom II X2 550 Black Edition 24.242 AMD Athlon II X4 620 27.722 AMD Athlon II X2 250 25.007 32 Million Digits (3 thread): (sec) Ranking Intel Core i7 920 23.297 AMD Phenom II X4 965 Black Edition 15.211 AMD Phenom II X4 955 Black Edition 15.46 AMD Phenom II X3 720 Black Edition (DDR2) 18.219 AMD Phenom II X3 720 Black Edition (DDR3) 17.936 AMD Athlon II X4 620 18.846 32 Million Digits (4 thread): (sec) Ranking Intel Core i7 920 13.954 AMD Phenom II X4 965 Black Edition 11.639 AMD Phenom II X4 955 Black Edition 11.84 AMD Athlon II X4 620 14.5854 32 Million Digits (all thread): (sec) Ranking Intel Core i7 920 9.547 Intel Core 2 Duo E8500 25.49 Intel Core 2 Duo E8400 27.078 AMD Phenom II X4 965 Black Edition 11.639 AMD Phenom II X4 955 Black Edition 11.84 AMD Phenom II X3 720 Black Edition (DDR2) 18.219 AMD Phenom II X3 720 Black Edition (DDR3) 17.936 AMD Phenom II X2 550 Black Edition 24.242 AMD Athlon II X4 620 14.585 AMD Athlon II X2 250 25.007

This is where you can really see the effect of multi-core scaling. The $99 AMD Athlon II X4 620 processor starts off as the slowest single-threaded processor, but when all of its cores are put to use it's ~3 seconds behind the Phenom II X4s and ~5 seconds behind the $300 Core i7 920 processor.

wPrime 2.0 - Windows 7 32 Million Digits (1 thread): (sec) Ranking Intel Core i7 920 50.672 Intel Core 2 Duo E8400 53.93 AMD Phenom II X4 965 Black Edition 44.025 AMD Athlon II X4 620 54.509 32 Million Digits (2 thread): (sec) Ranking Intel Core i7 920 25.531 Intel Core 2 Duo E8400 27.05 AMD Phenom II X4 965 Black Edition 21.964 AMD Athlon II X4 620 28.546 32 Million Digits (3 thread): (sec) Ranking Intel Core i7 920 16.984 AMD Phenom II X4 965 Black Edition 14.801 AMD Athlon II X4 620 18.813 32 Million Digits (4 thread): (sec) Ranking Intel Core i7 920 13.047 AMD Phenom II X4 965 Black Edition 11.375 AMD Athlon II X4 620 14.743 32 Million Digits (all thread): (sec) Ranking Intel Core i7 920 9.766 Intel Core 2 Duo E8400 27.05 AMD Phenom II X4 965 Black Edition 11.375 AMD Athlon II X4 620 14.743

Under Windows 7 the AMD Athlon II X4 620 continues to fair well in this mathematical benchmark. While its single core performance can't quite keep up the Intel Core 2 Duo E8400, with all four cores loaded up it can essentially double its performance, to 14 seconds..