That is, a number has no other factors except 1 and itself, otherwise it is called a composite number.
theorem
There must be at least one prime number between the number A greater than 1 and its twice (that is, within the interval (a, 2a)).
There is a prime arithmetic progression of arbitrary length.
An even number can be written as the sum of two numbers, and each number has at most nine prime factors.
Even numbers must be written as prime addition numbers, where there is an upper limit on the number of factors.
Even numbers must be written as a prime number plus a composite number consisting of at most five factors. Later, someone shortened this result to (1+5)?
A sufficiently large even number must be written as a prime number plus a composite number consisting of at most two prime factors. Short for (1+2)?
nature
The (1) prime p has only two divisors: 1 and p.
(2) Basic theorem of elementary mathematics: Any natural number greater than 1 is either a prime number itself or can be decomposed into the product of several prime numbers, and this decomposition is unique.
(3) The number of prime numbers is infinite.
(4) The number formula π(n) of prime numbers is an irreducible function.
(5) If n is a positive integer, from the second power of n to the second power of (n+ 1)? There is at least one prime number between.
(6) If n is a positive integer greater than or equal to 2, it is between n and n! There is at least one prime number between.
(7) If the prime number P is the largest prime number not exceeding n (n is greater than or equal to 4), then p & gtn/2? .