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The only prime belonging to two pairs of cousin primes is 7. One of the numbers n, n + 4, n + 8 will always be divisible by 3, so n = 3 is the only case where all three are primes. An example of a large proven cousin prime pair is (p, p + 4) for = + which has 20008 digits.
In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers. A positive integer which is not polite is called impolite . [ 1 ] [ 2 ] The impolite numbers are exactly the powers of two , and the polite numbers are the natural numbers that are not powers of two.
Farey sequences are very useful to find rational approximations of irrational numbers. [13] For example, the construction by Eliahou [14] of a lower bound on the length of non-trivial cycles in the 3x+1 process uses Farey sequences to calculate a continued fraction expansion of the number log 2 (3).
[1] [2] The integers 2 3 and 3 2 are two perfect powers (that is, powers of exponent higher than one) of natural numbers whose values (8 and 9, respectively) are consecutive. The theorem states that this is the only case of two consecutive perfect powers.
For any pair of positive integers n and k, the number of k-tuples of positive integers whose sum is n is equal to the number of (k − 1)-element subsets of a set with n − 1 elements. For example, if n = 10 and k = 4, the theorem gives the number of solutions to x 1 + x 2 + x 3 + x 4 = 10 (with x 1, x 2, x 3, x 4 > 0) as the binomial coefficient
And the numbers speak for themselves: Nvidia: if you invested $1,000 when we doubled down in 2009, you’d have $363,385 !* Apple: if you invested $1,000 when we doubled down in 2008, you’d have ...
70 is the fourth discrete sphenic number, as the first of the form . [1] It is the smallest weird number, a natural number that is abundant but not semiperfect, [2] where it is also the second-smallest primitive abundant number, after 20. 70 is in equivalence with the sum between the smallest number that is the sum of two abundant numbers, and the largest that is not (24, 46).
A Rhode Island man has admitted to using gasoline to set several fires around the exterior of a predominantly Black church earlier this year, according to a federal plea agreement.