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35 changes: 35 additions & 0 deletions C++/ISPRIME.cpp
Original file line number Diff line number Diff line change
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/*

Simple algorthiam to check Primality of a 32 bit int
Time complaxity : O(sqrt(n/3))
*/

#include <iostream>
#include <cassert>

using namespace std;
bool isPrime(int num)
{
if(num < 4) return n>1;

if(!(num&1) or num%3==0 ) return false;

for(int i=5;i*i<=num;i+=6)
if(num%i==0 or num%(i+2)==0)
return false;

return true;
}

int main()
{
int num;
cout<<"Enter number to check:";
cin>>num;
assert(num>0);
if(isPrime(num))
cout<< num <<" is Prime Number\n";
else
cout<< num <<" is not a Prime Number\n";

}
65 changes: 65 additions & 0 deletions C++/MillerRabin.cpp
Original file line number Diff line number Diff line change
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/*

Miller Ranbin test Deterministic method for checking a prime number;
Time Complexity : O(12*log(n));
Its Implementation

*/

#include<bits/stdc++.h>
using namespace std;
using u64 = uint64_t;
using u128 = __uint128_t;

u64 bin_exp(u64 base, u64 e, u64 mod) {
u64 result = 1;
base %= mod;
while (e) {
if (e & 1)
result = (u128)result * base % mod;
base = (u128)base * base % mod;
e >>= 1;
}
return result;
}

bool check_composite(u64 n, u64 a, u64 d, int s) {
u64 x = bin_exp(a, d, n);
if (x == 1 || x == n - 1)
return false;
for (int r = 1; r < s; r++) {
x = (u128)x * x % n;
if (x == n - 1)
return false;
}
return true;
};

bool MillerRabin(u64 n) {
if (n < 4)
return n > 1;

int r = 0; u64 d = n - 1;
while ((d & 1) == 0) {
d >>= 1,r++;
}

for (int a : {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}) {
if (n == a)
return true;
if (check_composite(n, a, d, r))
return false;
}
return true;
}
int main()
{
u64 num;
cout<<"Enter number to check:";
cin>>num;
assert(num>0);
if(MillerRabin(num))
cout<< num <<" is Prime Number\n";
else
cout<< num <<" is not a Prime Number\n";
}