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prime_testing.cpp
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prime_testing.cpp
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lld expo(lld a, lld n, lld p)
{
if(n==0)
return 1;
lld ex=expo(a,n/2,p);
if(n%2==1)
return (((ex*ex)%p)*a)%p;
else
return (ex*ex)%p;
}
bool miller_rabin(lld n, lld a)
{
if(n==2)
return true;
/*let n be the test value and 2<=a<=n-1. I find n-1=2^s*d. (a^d)%n=+1 or -1, return true; else check for (a^(2^i*d))%n=-1 for atleast one 2<=i<=s-1. If yes return true.*/
lld s,d,test;
if(a>n-1)
return true;
d=n-1;
s=0;
while(d%2==0)
s++, d=d/2;
test=expo(a,d,n);
if(test==1 || test==n-1)
return true;
while(s--)
{
test=expo(a,(1<<s)*d,n);
if(test==n-1)
return true;
}
return false;
}
bool prime_check(int i)
{
if(i==1)
return false;
if(i==2)
return true;
if(miller_rabin(i,2) && miller_rabin(i,3) && miller_rabin(i,5) && miller_rabin(i,7) && miller_rabin(i,11) && miller_rabin(i,13) && miller_rabin(i,17))
return true;
return false;
}