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According to Cator and Landsman, [4] Conway and Kochen prove that "determinism is incompatible with a number of a priori desirable assumptions". Cator and Landsman compare the Min assumption to the locality assumption in Bell's theorem and conclude in the strong free will theorem's favor that it "uses fewer assumptions than Bell’s 1964 ...
There are 4842 strong pseudoprimes base 2 and 2163 Carmichael numbers below this limit (see Table 1 of [5]). Starting at 17·257, the product of consecutive Fermat numbers is a base-2 pseudoprime, and so are all Fermat composites and Mersenne composites.
n 4 = n × n × n × n. Fourth powers are also formed by multiplying a number by its cube. Furthermore, they are squares of squares. Some people refer to n 4 as n tesseracted, hypercubed, zenzizenzic, biquadrate or supercubed instead of “to the power of 4”. The sequence of fourth powers of integers, known as biquadrates or tesseractic ...
They are listed in Table 7 of. [2] The smallest such number is 25326001. This means that, if n is less than 25326001 and n is a strong probable prime to bases 2, 3, and 5, then n is prime. Carrying this further, 3825123056546413051 is the smallest number that is a strong pseudoprime to the 9 bases 2, 3, 5, 7, 11, 13, 17, 19, and 23.
The problem of free will has been identified in ancient Greek philosophical literature. The notion of compatibilist free will has been attributed to both Aristotle (4th century BCE) and Epictetus (1st century CE): "it was the fact that nothing hindered us from doing or choosing something that made us have control over them".
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 real numbers can be defined synthetically as an ordered field satisfying some version of the completeness axiom.Different versions of this axiom are all equivalent in the sense that any ordered field that satisfies one form of completeness satisfies all of them, apart from Cauchy completeness and nested intervals theorem, which are strictly weaker in that there are non Archimedean fields ...
A proof of the level 1 and small weight cases of the conjecture was obtained in 2004 by Chandrashekhar Khare and Jean-Pierre Wintenberger, [3] and by Luis Dieulefait, [4] independently. In 2005, Chandrashekhar Khare obtained a proof of the level 1 case of Serre conjecture, [ 5 ] and in 2008 a proof of the full conjecture in collaboration with ...