using namespace std;
cout<<"Enter thenumber till the check should go";
Avoid that code above. First of all it doesn't work at all, aside from that, main has no return type, and has no return value either, and that's bad, very bad. Using system("pause") is also not recommended, use cin.get() instead.
This statement only checks if a number can be divided by 2, 3, 5, 7. I can easily make up numbers that are not primes yet cannot be divided by 2 3 5 7. In fact any multiplication of prime numbers above 7 will be missed. Starting from 11, the wider the range the more you miss.
who told you that 121 is a prime number oh please
besides the code i have written works perfectly fine and i have tested it a hundred times
and i can pretty easily guess that you are a noob at c++ as this code is made for dev c++ compiler which is popular nowadays
>>in the interval [x,y] how many numbers have exactly 14 divisors
24 has 16 integer divisors: 24, 1, 12, 2, 8, 3, 6, 4 (and respective negative ints)
24 has 8 positive integer divisors
24 has 2 prime divisors: 2 and 3, assuming the definition of prime divisors is divisors that are prime (and if you accept the definition that 1 isn't a prime number).
I know of no short cut way to determine the number of postive integer divisors a number has, except to say if the number is prime, then the number of divisors is 2. Maybe someone is aware of a nifty algorhithm to determine the number of positive integer divisors any given positive integer has. I'd use brute force.
Mark me wrong, but a sieve for 8k numbers shouldn't run too long.
Why 8k? It's sqrt(64000000) and all divisors are mirrored after square root, ie:
Divisors of 28: 1,2,4,7,14,28. You can connect them in pairs: 1-28,2-14,4-7. And guess what? Left and right sides of the pair are parted by sqrt(28).
To make myself clear: if you want exactly 14 divisors (are they proper?) of a number, just check, if there are exactly seven divisors <sqrt(number).
At this point, all you need to do is make some optimalizations, like if a number is a square of an integer, there is a connection between it's and it's sqrt's divisors and so on.
actually that is partly incorrect because for a number to have 14 divisors it must be of this form : p1*p2^6 where p1 and p2 are prime numbers i have tried setting an upper and bottom limit for p2 and analyzing the prime numbers but it too slow