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Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics.It states that every even natural number greater than 2 is the sum of two prime numbers.
38 is the sum of the squares of the first three primes. 37 and 38 are the first pair of consecutive positive integers not divisible by any of their digits. 38 is the largest even number which cannot be written as the sum of two odd composite numbers. The sum of each row of the only non-trivial (order 3) magic hexagon is 38. [4]
Montgomery and Vaughan showed that the exceptional set of even numbers not expressible as the sum of two primes has a density zero, although the set is not proven to be finite. [9] The best current bounds on the exceptional set is E ( x ) < x 0.72 {\displaystyle E(x)<x^{0.72}} (for large enough x ) due to Pintz , [ 10 ] [ 11 ] and E ( x ) ≪ x ...
Even numbers are always 0, 2, or 4 more than a multiple of 6, while odd numbers are always 1, 3, or 5 more than a multiple of 6. ... like the Kissing Number Problem. ... For example, x²-6 is a ...
The number is taken to be 'odd' or 'even' according to whether its numerator is odd or even. Then the formula for the map is exactly the same as when the domain is the integers: an 'even' such rational is divided by 2; an 'odd' such rational is multiplied by 3 and then 1 is added.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
It turns out that for some values of the limit (such as values a bit more than 906 million), [25] [26] most numbers less than the limit have an even number of prime factors. Erik Christopher Zeeman tried for 7 years to prove that one cannot untie a knot on a 4-sphere. Then one day he decided to try to prove the opposite, and he succeeded in a ...
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