A Cullen number has the form \(C_k = k \cdot 2^k + 1\). The sequence starts 3, 9, 25, 65, 161, 385, 897, 2049, 4609.
Named for Father James Cullen, an Irish Jesuit who studied them in 1905. Almost all Cullen numbers are composite; Cullen primes are exceptional — the only known small one is \(C_1 = 3\), with the next at \(k = 141\), and only a handful more found despite extensive distributed searches.