Start: For n=100170 to 300000, For k=1 to 1 step 1, Probable Prime. Stop: n=100641, k=1. Start: For n=1 to 1, For k=1 to 1 step 1, Probable Prime. 250000000000........000000000001 is probable prime! (a = 35461) (digits:9292) 250000000000........000000000001 is probable prime! (verification : a = 35509) (digits:9292) Start: For n=1 to 1, For k=1 to 1 step 1, N-1 Test. 250000000000........000000000001 is prime! [N-1, Brillhart-Lehmer-Selfridge] (digits:9292) 250000000000........000000000001(digits:9292 checksum:_A80DB786_) "Brillhart-Lehmer-Selfridge theorems. If the conditions above hold and F is greater than the square root of N, then N is surely prime. (Proth's theorem is a special case of this). If F is greater than the cube root of N, N is the product of at most two primes, a possibility that can be tested by a perfect square test."