\\
\\---------------------------------------------------------------------------------
\\ A program that searches Mersenne prime
\\---------------------------------------------------------------------------------
\\	input: YES  -  ll(n)   nth Mersenne prime  -   Lucas–Lehmer primality test 
\\---------------------------------------------------------------------------------
\\	input: YES  -  mer(n)  nth Mersenne prime  -   New test
\\---------------------------------------------------------------------------------
\\
\\
\\------------------------------------------------------------------------------------
\\	allocatemem(4096000000);
\\------------------------------------------------------------------------------------
\\
LL(p)={
	my(m=Mod(4,1<<p-1));
	for(i=3,p,m=m^2-2);
	m==0;
}
\\
\\------------------------------------------------------------------------------------
\\ 
ll(maxt)={
	my(t=1);
\\
	print("\ni=",1,"  2^2-1");
	forprime(p=3,74207281,
		if(LL(p),
			print("i=",t+1,"  2^"p"-1");
			if(t++==maxt,print(" ");return());
		);
	);
}
\\
\\------------------------------------------------------------------------------------
\\------------------------------------------------------------------------------------
\\
mer(maxi)={
	local(i,mer,ex,p,m4,k);
\\
	print(" ");
\\
	i=3;
	forprime(p=3,74207281,
		ex=2^p;
		mer=ex-1;
		ex=ex>>1;
		k=Mod(2^((p+3)/2)+2,mer);
		m4=Mod(4+k^2,mer);
		y=m4^ex;
		if(y==m4,print("i=",i,"  MER_p=",p);if(i==maxi,print(" ");return());i++);
	);
\\
	print(" ");
	return();
\\
}
\\
\\------------------------------------------------------------------------------------
\\------------------------------------------------------------------------------------