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Is there at least one prime number in 20 consecutive natural numbers right Don't forget to say the reason
This is wrong
Let 21! = 1 * 2 * 3 *... * 20 * 21, then 20 consecutive natural numbers 21! + 2,21! + 3,... 21! + 21 are not prime numbers: for example, 21! + 3 = 3 * (1 * 2 * 4 * 5 *... * 21) + 3 = 3 * (1 * 2 * 4 * 5 *... * 21 + 1). The same method can prove that for any n, all consecutive n natural numbers are not prime numbers
What is the difference between even numbers that are not prime numbers in natural numbers 1 to 20
In natural numbers 1 to 20, even numbers that are not prime numbers are 4,6,8,10,12,14,16,18,20
If n is a natural number, N + 3 and N + 7 are prime numbers, find the remainder of N divided by 3
If the remainder is 0, that is, n = 3K (k is a non negative integer, the same below), then n + 3 = 3K + 3 = 3 (K + 1), so 3|n + 3 and 3 ≠ n + 3, so n + 3 is not a prime number, which is in contradiction with the proposition. ② if the remainder is 2, and N = 3K + 2, then n + 7 = 3K + 2 + 7 = 3 (K + 3), so 3|n + 7 and N + 7 are not prime numbers, which is in contradiction with the proposition The number can only be 1
RELATED INFORMATIONS
- 1. If n is a natural number, N + 3 and N + 7 are prime numbers, find the remainder of N divided by 3
- 2. When n = 1,2,3,4, the value of square + N + 41 of n is prime. Please write two values of N less than 45 so that square + N + 41 of n is not prime
- 3. What is the product of natural numbers less than 10 that are not prime numbers
- 4. There is a prime in two natural numbers. These two are coprime numbers, right?
- 5. () and any non-zero natural number can form coprime numbers; the product of two prime numbers must be ()
- 6. Write two continuous natural numbers that are combined numbers______ And______ ．
- 7. A natural number can be decomposed into the product of three prime factors. If the sum of the squares of the three prime factors is 1710, how to find the natural number?
- 8. What is the square of the two differences of equation 3yy-2y-2 = 0?
- 9. 7Y = y + 1 solve equations,
- 10. The square numbers of natural numbers are arranged in descending order: 14916236496481100.. what is the 351st digit?
- 11. Two numbers are compound numbers and coprime numbers. Their least common multiple is 120. The greatest common divisor of these two numbers is______ Where the smaller sum is______ ．
- 12. The composite of two coprime numbers, their least common multiple is 72, the two composite numbers are
- 13. In the natural numbers smaller than 10, the numbers whose two adjacent numbers are prime numbers are () and (), and the numbers whose two adjacent numbers are combined numbers are () and ()
- 14. Use the prime number of two digits of 1,5,6 (), sum number (), multiple of 2 (), multiple of 3 (), multiple of 5 (), which is not only a multiple of 3 but also a multiple of 5
- 15. 1. The sum of 5 and 6 is the prime number, the multiple of 2, the multiple of 3, the multiple of 5, the multiple of 3 and the multiple of 5?
- 16. Is 111 prime
- 17. The product of the two prime numbers is 111. The two prime numbers are () and ()
- 18. 2,3,4,5 can form () 7, for coprime
- 19. Among the four numbers 2, 3, 4 and 5, they can be coprime numbers__ yes
- 20. Proof: if n > 1 and a ^ n - 1 is prime, then a = 2 and N is prime