> 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 > > Hello Max, > 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) ? Note that P(2)=7 & P(3)=43, so I think your question should be: Can anybody prove that P(p) can never be prime for prime p, p>3 or find prime P(p) for some prime p>3 (in which case p must be > 150000) ? I will think to your question. Best wishes, Farideh
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