https://sourceforge.net/p/isitprime/wiki/Testing%2520Methods/Recent changes to Testing MethodsenThu, 30 Aug 2012 14:09:50 -0000https://sourceforge.net/p/isitprime/wiki/Testing%2520Methods/As of IsItPrime 1.6.0, there are several ways to test any given number. As of version 1.7.0, these methods have been both expanded and improved. Brute-Force Trial Division, or BFTD, is the slowest and most accurate method of testing for prime numbers. It does exactly what it sounds like it does - divides the candidate number by every number possible, starting at 2 and working up until it reaches the candidate number itself. This is great for most numbers, but past a certain size, BFTD is far too inefficient. Small Prime Array Testing, or SPAT, is fast and inaccurate - however, it is good for determining very quickly if a number has small factors. It tests only prime factors, as those are statistically the most likely to occur in composite numbers. However, it should _not_ be used to determine primality in an absolute sense, as most numbers reported as "prime" by SPAT are in fact false-positives. In addition to these two main methods, there are two testing modes - verbose and non-verbose. Verbose mode displays all factors found for the number, whereas non-verbose mode stops after finding only one. This is helpful if your primary goal is to factor a number you know to be composite. It also helps enforce compositeness by finding and displaying the same factor twice (a and quotient b, then b and quotient a). There are also two testing ranges - up to n (up to the candidate number) and up to the square root of n. The testing methods available in version 1.7.0 are as follows: * BFTD, up to n, verbose mode * BFTD, up to n, non-verbose mode * BFTD, up to sqrt, verbose mode * BFTD, up to sqrt, non-verbose mode * SPAT, up to first 100 primes, verbose mode * SPAT, up to first 500 primes, verbose mode Most of these are triple-threaded. This makes the tests faster but also considerably more CPU-intensive. Please bear this in mind!Jaska BörnerThu, 30 Aug 2012 14:09:50 -0000https://sourceforge.netbe1ed07ea75345e2777a1a4102aeca509c375bd7