Hello! This problem is somewhat related to Mersenne numbers.
Let p be a prime number and q = 2^p - 1 (so q is a Mersenne number but not necessary prime). Can the number q^2 - q + 1 be prime? Substituting the value for q, we can formulate the same problem as follows: Can the number P(p) = 2^(2*p) - 3*2^p + 3 be prime for prime p? What is known: If p is not limited to primes, then there are many primes P(p). There are also many primes P(p) if p is limited to powers of primes. But no prime P(p) found for primes p < 150000. Can anybody prove that P(p) can never be prime for prime p or find prime P(p) for some prime p (in which case p must be > 150000) ? Thanks, Max P.S. The origin of this problem (in russian): http://www.nsu.ru/phorum/read.php?f=29&i=5095&t=5095 _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
