Two, three, five, seven, eleven, one followed by three, nine, three, five, five, three, three, seven followed by one, three, seven followed by one, three, nine, eight, three, eight, nine, seven.

Prime numbers, also called prime numbers, are infinite. The definition of prime number means that among natural numbers greater than 1, there are no other factors except 1 and itself, and there are 25 prime numbers within 100.

They are: 2, 3, 5, 7,1,13, 17, 19, 23, 29, 3 1, 37, 4/kloc.

Extended data:

The number of prime numbers is infinite. There is a classic proof in Euclid's Elements of Geometry. It uses a common proof method: reduction to absurdity. The concrete proof is as follows: suppose there are only a limited number of n prime numbers, which are arranged in the order of p 1, p2, ..., pn, and let n = p1× p2××××× pn.

So, is N+ 1 a prime number? If N+ 1 is a prime number, then N+ 1 is greater than p 1, p2, ..., pn, so it is not in those assumed prime number sets.

1, if it is a composite number, because any composite number can be decomposed into the product of several prime numbers; The greatest common divisor of n and N+ 1 is 1, so it is impossible to be divisible by p 1, p2, ..., pn, so the prime factor obtained by this complex number decomposition is definitely not in the assumed prime number set. So whether this number is prime or composite.

It means that there are other prime numbers besides the assumed finite number of prime numbers. So the original assumption doesn't hold water. In other words, there are infinitely many prime numbers.

2. Other mathematicians have given some different proofs. Euler proved by Riemann function that the sum of reciprocal of all prime numbers is divergent, Ernst Cuomo proved more succinctly, and harry Furstenberg proved by topology.

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