Palimar, S.Shankar, B.R.2026-02-052012Journal of Integer Sequences, 2012, 15, 5, pp. -15307638https://idr.nitk.ac.in/handle/123456789/26999The concept of Mersenne primes is studied in real quadratic fields with class number one. Computational results are given. The field ?(?2) is studied in detail with a focus on representing Mersenne primes in the form x2 + 7y2. It is also proved that x is divisible by 8 and y ? ±3 (mod 8), generalizing a result of F. Lemmermeyer, first proved by H. W. Lenstra and P. Stevenhagen using Artin's reciprocity law.Artin's reciprocity lawMersenne primes