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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 ...
Ω(n), the prime omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities). A prime number has Ω( n ) = 1. The first: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 (sequence A000040 in the OEIS ).
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.
Semiprime numbers have no composite numbers as factors other than themselves. [6] For example, the number 26 is semiprime and its only factors are 1, 2, 13, and 26, of which only 26 is composite.
Goldbach's comet; red, blue and green points correspond respectively the values 0, 1 and 2 modulo 3 of the number. The Goldbach partition function is the function that associates to each even integer the number of ways it can be decomposed into a sum of two primes. Its graph looks like a comet and is therefore called Goldbach's comet. [30]
a prime number has only 1 and itself as divisors; that is, d(n) = 2 a composite number has more than just 1 and itself as divisors; that is, d ( n ) > 2 a highly composite number has a number of positive divisors that is greater than any lesser number; that is, d ( n ) > d ( m ) for every positive integer m < n .
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 ...
Furthermore, if b 1, b 2 are both coprime with a, then so is their product b 1 b 2 (i.e., modulo a it is a product of invertible elements, and therefore invertible); [6] this also follows from the first point by Euclid's lemma, which states that if a prime number p divides a product bc, then p divides at least one of the factors b, c.