Prime numbers are also called prime numbers. A natural number greater than 1 cannot be divisible by other natural numbers except 1 and itself, and is called a prime number; Otherwise it is called a composite number.
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 prime numbers, which are arranged as p 1, p2, ..., pn from small to large, and let N = P 1× P2×...× PN, then is N+ 1 a prime number?
Extended data:
First, the interval law of prime number distribution
S 1 interval 1-72, with 18 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. )
S2 interval 73-2 16 has 27 prime numbers and 7 pairs of twin prime numbers.
S3 interval 2 17-432 has 36 prime numbers and 8 pairs of twin prime numbers.
S4 interval 433-720 has 45 prime numbers and 7 pairs of twin prime numbers.
S5 interval is 721-1080, with 52 prime numbers and 8 pairs of double prime numbers.
S6 interval1081-1512, with 60 prime numbers and 9 pairs of twin prime numbers.
S7 interval1513—2016,65 prime numbers,1/twin prime numbers.
The S8 interval is 20 17-2592, with 72 prime numbers and 12 pairs of twin prime numbers.
S9 interval is 2593-3240, 80 prime numbers, 10 pairs of twin prime numbers.
S 10 interval 3241-3960, 9 1 prime, 19 pairs of twin prime numbers.
There are 92 prime numbers in the interval S 1 1-4752, and 17 pairs of twin prime numbers.
S 12 interval 4752-5616 has 98 prime numbers, and 13 pairs of twin prime numbers.
S 13 interval 5617-6552 prime 108, twin prime 14 pairs.
S 14 interval 6553-7560 primes 1 13, twin primes 19 pairs.
S 15 interval 7561-8640 prime 1 16, twin prime 14 pairs.
Second, related applications
Prime numbers are used in cryptography. The so-called public key is to add a prime number to the information to be transmitted when encoding, and then transmit it to the receiver after encoding. If anyone receives this information without the key possessed by the receiver, the process of decryption (actually the process of finding prime numbers (decomposing prime factors)) will be too long, even making it meaningless to obtain information.
In the design of automobile gearbox gears, the number of teeth of two adjacent gears is designed as prime numbers, so as to increase the least common multiple of the number of encounters and meshing of two identical teeth in two gears, which can enhance durability and reduce failures.
The relationship between the biological growth cycle of pests and the use of pesticides has also been proved. Experiments show that it is the most reasonable to use pesticides many times: they are all used in the climax of pest reproduction, and it is difficult for pests to produce drug resistance.
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