how to calculate prime numbers

how to calculate prime numbers Is there any way or function to find out the number of primes numbers up to any number Say 10 7 or 10 30 or 200 or 300

Is there any function to evaluate the number of prime numbers between 2 n For example consider the following range 2 20 In this case the number of prime numbers between 2 and 20 is 8 2 3 5 7 11 13 17 19 Therefore the function I m looking for would return 8 begingroup The general approach to find large prime numbers is to sieve out small factors to get candidates numbers that might be prime before testing whether they are actually prime This is rather time consuming for very large numbers and the chance to be successful is small even if we sieve out the prime factors upto 10 9 or so

how to calculate prime numbers

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how to calculate prime numbers
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Int count primes between int x int y i is used to loop all numbers from x to y j is used to iterate over each number in the range specified by x and y count stores the number of primes int j i count 0 int f 0 f stores number of factors of each number for i x i Now if you re trying to compute the nth prime it has been proven that the nth prime must be greater than nlog n n loglog n 1 and less than nlog n nlog log n When n 6 So if you re searching for the nth prime you can use these ranges to search the nth prime number Here you can use binary search to get the nth Prime number

There is also an order in which numbers other than prime numbers appear so 7x5 then 7x7 then 7x11 then 7x13 then 7x19 etc Prime numbers greater than 7 such as 11 and 13 are also 11 5 13 5 11 7 13 7 It will appear on the table as 11 11 13 13 etc enter image description here yellow is for prime numbers Is there any algorithm or a technique to calculate how many prime numbers lie in a given closed interval a1 an knowing the values of a1 and an with a1 an Example 2 10 4 prime numbers 2 3 5 7

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begingroup Dear picakhu I don t know the best worst case bound for a deterministic algorithm but on average if you keep trying random numbers in 0 N you ll need about log N trials to find a prime number Each trial can be done in polylogarithmic space using either a randomized or deterministic algorithm Take each number within the given range Take the square root of the largest number in this range If a number is prime it will not be divisible by any numbers smaller than the square root of this largest number Now take out all the numbers divisible by 2 Then all the numbers divisible by 3

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