Search results
Results from the WOW.Com Content Network
The first such distribution found is π(N) ~ N / log(N) , where π(N) is the prime-counting function (the number of primes less than or equal to N) and log(N) is the natural logarithm of N. This means that for large enough N, the probability that a random integer not greater than N is prime is very close to 1 / log(N).
Define, for real m and for natural numbers n and k, P k (m,n) as the number of numbers not greater than m with exactly k prime factors, all greater than p n. Furthermore, set P 0 (m,n) = 1. Then (,) = = + (,) where the sum actually has only finitely many nonzero terms.
p n # as a function of n, plotted logarithmically.. For the n th prime number p n, the primorial p n # is defined as the product of the first n primes: [1] [2] # = =, where p k is the k th prime number.
This is a list of articles about prime numbers. A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes.
A plot of the number of digits in the largest known prime by year, since the electronic computer. The vertical scale is logarithmic. A prime number is a natural number greater than 1 with no divisors other than 1 and itself. According to Euclid's theorem there are infinitely many prime numbers, so there is no largest prime.
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a ...
Euler ascertained that 2 31 − 1 = 2147483647 is a prime number; and this is the greatest at present known to be such, and, consequently, the last of the above perfect numbers [i.e., 2 30 (2 31 − 1)], which depends upon this, is the greatest perfect number known at present, and probably the greatest that ever will be discovered; for as they ...
The smallest integer m > 1 such that p n # + m is a prime number, where the primorial p n # is the product of the first n prime numbers. A005235: Semiperfect numbers: 6, 12, 18, 20, 24, 28, 30, 36, 40, 42, ... A natural number n that is equal to the sum of all or some of its proper divisors. A005835: Magic constants