2、3、5、7、 1 1、 13、 17、 19、23、29、3 1、37、4 1、43、47、53、59、6 1、67、7 1、73、79、83、89、97。

One * * * has 25.

1, there must be at least one prime number between a number greater than 1 and its twice (that is, within the interval (a, 2a)).

2. There is a prime arithmetic progression of any length.

3. An even number can be written as the sum of two composite numbers, and each composite number has at most 9 prime factors. (Norwegian mathematician Brown, 1920)

4. Even numbers must be written as prime numbers plus composite numbers, in which the number of factors of composite numbers has an upper bound. (Renee, 1948)

5. Even numbers must be written as a prime number plus a composite number consisting of at most five factors.

6. A sufficiently large even number must be written as a prime number plus a composite number consisting of at most two prime factors.

Extended data:

Between 1 and S 1, there are 1-72 prime numbers and 7 pairs of twin prime numbers. (2 and 3 are not counted, and the last number of twins is also counted in the previous interval. )

2.S2 interval 73-2 16, 27 prime numbers and 7 pairs of twin prime numbers.

3.S3 interval is 217-432, with 36 prime numbers and 8 pairs of double prime numbers.

4.S4 interval 433-720, 45 prime numbers, 7 pairs of double prime numbers.

5.S5 interval is 721-1080, with 52 prime numbers and 8 pairs of double prime numbers.

6.S6 interval1081—1512,60 prime numbers and 9 pairs of twin prime numbers.

7.S7 interval1513—2016,65 prime numbers,1/twin prime numbers.

8. The 8.S8 interval is 20 17-2592, with 72 prime numbers and 12 pairs of twin prime numbers.

In the S9 interval of 9.2593-3240, there are 80 prime numbers, 10 pairs of twin prime numbers.

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