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35 has two prime factors, (5 and 7) which also form its main factor pair (5 x 7) and comprise the second twin-prime distinct semiprime pair. The aliquot sum of 35 is 13, within an aliquot sequence of only one composite number (35,13,1,0) to the Prime in the 13-aliquot tree. 35 is the second composite number with the aliquot sum 13; the first ...
m is a divisor of n (also called m divides n, or n is divisible by m) if all prime factors of m have at least the same multiplicity in n. The divisors of n are all products of some or all prime factors of n (including the empty product 1 of no prime factors). The number of divisors can be computed by increasing all multiplicities by 1 and then ...
The semiprimes are the case = of the -almost primes, numbers with exactly prime factors. However some sources use "semiprime" to refer to a larger set of numbers, the numbers with at most two prime factors (including unit (1), primes, and semiprimes). [3]
There are 808,675,888,577,436 twin prime pairs below 10 18. [20] [21] An empirical analysis of all prime pairs up to 4.35 × 10 15 shows that if the number of such pairs less than x is f (x) ·x /(log x) 2 then f (x) is about 1.7 for small x and decreases towards about 1.3 as x tends to infinity.
All pairs of positive coprime numbers (m, n) (with m > n) can be arranged in two disjoint complete ternary trees, one tree starting from (2, 1) (for even–odd and odd–even pairs), [10] and the other tree starting from (3, 1) (for odd–odd pairs). [11] The children of each vertex (m, n) are generated as follows:
More generally, a positive integer c is the hypotenuse of a primitive Pythagorean triple if and only if each prime factor of c is congruent to 1 modulo 4; that is, each prime factor has the form 4n + 1. In this case, the number of primitive Pythagorean triples (a, b, c) with a < b is 2 k−1, where k is the number of distinct prime factors of c ...
A 1.35 factor rate is a mid-range rate lenders charge to borrow money. Factor rates typically fall between 1.1 and 1.5. With a 1.35 factor rate, it will cost $35,000 to borrow $100,000 ($100,000 x ...
However, amicable numbers where the two members have different smallest prime factors do exist: there are seven such pairs known. [8] Also, every known pair shares at least one common prime factor. It is not known whether a pair of coprime amicable numbers exists, though if any does, the product of the two must be greater than 10 65.