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No Yes Free Java Any DREAM: Real-time C++, Timed automata: Monitor automata Yes No No No Free C++: Windows, Unix related FizzBee Specification Language Plain and probabilistic Python: LTL: Yes Yes No Yes Free Go: macOS, Windows, Linux Java Pathfinder: Plain and timed Java unknown No Yes No No Open Source Agreement Java: macOS, Windows, Linux ...
A composite number n is a strong pseudoprime to at most one quarter of all bases below n; [3] [4] thus, there are no "strong Carmichael numbers", numbers that are strong pseudoprimes to all bases. Thus given a random base, the probability that a number is a strong pseudoprime to that base is less than 1/4, forming the basis of the widely used ...
Certain number-theoretic methods exist for testing whether a number is prime, such as the Lucas test and Proth's test. These tests typically require factorization of n + 1, n − 1, or a similar quantity, which means that they are not useful for general-purpose primality testing, but they are often quite powerful when the tested number n is ...
For example, n=5777 is a strong psp base 76, and is also a strong Lucas pseudoprime. No composite number below 2 64 (approximately 1.845·10 19) passes the strong or standard Baillie–PSW test, [3] that result was also separately verified by Charles Greathouse in June 2011. Consequently, this test is a deterministic primality test on numbers ...
For these numbers, repeated application of the Fermat primality test performs the same as a simple random search for factors. While Carmichael numbers are substantially rarer than prime numbers (Erdös' upper bound for the number of Carmichael numbers [ 3 ] is lower than the prime number function n/log(n) ) there are enough of them that Fermat ...
Input #1: b, the number of bits of the result Input #2: k, the number of rounds of testing to perform Output: a strong probable prime n while True: pick a random odd integer n in the range [2 b −1 , 2 b −1] if the Miller–Rabin test with inputs n and k returns “ probably prime ” then return n
No; proprietary — C, C++ Java, JSP JavaScript .NET Python ColdFusion, ASP, PHP, Perl, Visual Basic 6, PL/SQL, T-SQL, COBOL Analyzes source code to identify security vulnerabilities while integrating security testing with software development processes and systems. Helix QAC: 2023-04 (2023.1) No; proprietary — C, C++ — — — — —
In number theory, a narcissistic number [1] [2] (also known as a pluperfect digital invariant (PPDI), [3] an Armstrong number [4] (after Michael F. Armstrong) [5] or a plus perfect number) [6] in a given number base is a number that is the sum of its own digits each raised to the power of the number of digits.