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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.
No even number greater than 2 is prime because any such number can be expressed as the product /. Therefore, every prime number other than 2 is an odd number, and is called an odd prime. [9] Similarly, when written in the usual decimal system, all prime numbers larger than 5 end in 1, 3, 7, or 9. The numbers that end with other digits are all ...
In 1930, Lev Schnirelmann proved that any natural number greater than 1 can be written as the sum of not more than C prime numbers, where C is an effectively computable constant; see Schnirelmann density. [11] [12] Schnirelmann's constant is the lowest number C with this property. Schnirelmann himself obtained C < 800 000.
In mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the factors. [3][4][5] For example, The theorem says two things about this example: first ...
For example, π(10) = 4 because there are four prime numbers (2, 3, 5 and 7) less than or equal to 10. The prime number theorem then states that x / log x is a good approximation to π(x) (where log here means the natural logarithm), in the sense that the limit of the quotient of the two functions π(x) and x / log x as x increases without ...
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. Many of the largest known primes are Mersenne primes , numbers that are one less than a power of two, because they can utilize a specialized primality ...
Let π(x) be the prime-counting function that gives the number of primes less than or equal to x, for any real number x. The prime number theorem then states that x / log x is a good approximation to π ( x ) , in the sense that the limit of the quotient of the two functions π ( x ) and x / log x as x increases without bound is 1:
A prime gap is the difference between two successive prime numbers. The n -th prime gap, denoted gn or g (pn) is the difference between the (n + 1)-st and the n -th prime numbers, i.e. We have g1 = 1, g2 = g3 = 2, and g4 = 4. The sequence (gn) of prime gaps has been extensively studied; however, many questions and conjectures remain unanswered.