The exact number of prime numbers between 50 and 1000 is 153.
Understanding Prime Numbers Between 50 and 1000
To determine the number of prime numbers between 50 and 1000, we need to count all primes starting from 51 up to 999. This can be calculated by finding the total number of prime numbers up to 1000 and subtracting the number of primes that are 50 or less.
Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves.
- Total Prime Numbers up to 1000: There are 168 prime numbers from 1 to 1000.
- Prime Numbers up to 50: The prime numbers less than or equal to 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. There are 15 primes in this range.
Therefore, the number of prime numbers between 50 and 1000 is:
168 (primes up to 1000) - 15 (primes up to 50) = 153.
Detailed Breakdown of Prime Numbers by Range
The distribution of prime numbers varies across different intervals. The complete list of prime numbers from 1 to 1000, as referenced from sources like BYJU'S, provides a clear overview.
Below is a table illustrating the count of prime numbers within specific ranges, highlighting those mentioned in the provided reference:
| Range | Number of Prime Numbers | Notes |
|---|---|---|
| 1-50 | 15 | Primes less than or equal to 50 |
| 51-100 | 10 | |
| 101-200 | 21 | |
| 201-300 | 16 | |
| 301-400 | 16 | |
| 401-500 | 17 | |
| 501-600 | 14 | Information from provided reference |
| 601-700 | 16 | Information from provided reference |
| 701-800 | 14 | Information from provided reference |
| 801-900 | 15 | Information from provided reference |
| 901-1000 | 14 | |
| Total (51-1000) | 153 | Sum of primes between 50 and 1000 |
| Total (1-1000) | 168 |
By summing the number of primes in the ranges from 51-100, 101-200, 201-300, 301-400, 401-500, 501-600, 601-700, 701-800, 801-900, and 901-1000, we arrive at the total of 153 primes between 50 and 1000.
