is prime for , 458329, 942841, 966289, 1510441, ... (OEIS A135430). These values are also known as Lehmer-Ramanujan numbers or LR numbers since the first of them was found by Lehmer (1965). The corresponding primes have explicit values given by , , ... (OEIS A265913).
It is known that if is prime, then must be an odd square.
Large values of for which is a (probable) prime are summarized in the table below (Lifchitz and Lifchitz).
decimal digits | discoverer | |
180524 | N. Lygeros and O. Rozier (May 2015) | |
258571 | N. Lygeros and O. Rozier (May 2015) | |
282048 | N. Lygeros and O. Rozier (May 2015) | |
498503 | N. Lygeros and O. Rozier (May 2015) | |
555339 | N. Lygeros and O. Rozier (Sep. 2015) |