Ad
related to: the strong free will theorem calculator 2 decimal numbers 10solvely.ai has been visited by 10K+ users in the past month
Search results
Results From The WOW.Com Content Network
The free will theorem states: Given the axioms, if the choice about what measurement to take is not a function of the information accessible to the experimenters (free will assumption), then the results of the measurements cannot be determined by anything previous to the experiments. That is an "outcome open" theorem:
Specifically, Kim and Pomerance showed the following: The probability that a random odd number n ≤ x is a Fermat pseudoprime to a random base < < is less than 2.77·10 −8 for x= 10 100, and is at most (log x) −197 <10-10,000 for x≥10 100,000.
Compared with the fixed-point number system, the floating-point number system is more efficient in representing real numbers so it is widely used in modern computers. While the real numbers R {\displaystyle \mathbb {R} } are infinite and continuous, a floating-point number system F {\displaystyle F} is finite and discrete.
Safe primes ending in 7, that is, of the form 10n + 7, are the last terms in such chains when they occur, since 2(10n + 7) + 1 = 20n + 15 is divisible by 5. For a safe prime, every quadratic nonresidue, except -1 (if nonresidue [a]), is a primitive root. It follows that for a safe prime, the least positive primitive root is a prime number. [15]
There are some tests for numbers of the form k 2 m + 1, such as factors of Fermat numbers, for primality. Proth's theorem (1878). Let N = k 2 m + 1 with odd k < 2 m. If there is an integer a such that / then is prime. Conversely, if the above congruence does not hold, and in addition
Using fast algorithms for modular exponentiation and multiprecision multiplication, the running time of this algorithm is O(k log 2 n log log n) = Õ(k log 2 n), where k is the number of times we test a random a, and n is the value we want to test for primality; see Miller–Rabin primality test for details.
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
The prime number theorem asserts that an integer m selected at random has roughly a 1 / ln m chance of being prime. Thus if n is a large even integer and m is a number between 3 and n / 2 , then one might expect the probability of m and n − m simultaneously being prime to be 1 / ln m ln(n − m) .