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Cullen Number

Definition

A Cullen number is a number of the form C_n = 2^n n + 1. The first few are 3, 9, 25, 65, 161, 385, ... (OEIS A002064). Cullen numbers are divisible by p = 2n - 1 if p is a prime of the form 8k ± 3. The first few prime Cullen numbers are numbers 3, 393050634124102232869567034555427371542904833, ... (OEIS A050920), corresponding to n = 1, 141, 4713, 5795, 6611, 18496, 32292, 32469, 59656, 90825, 262419, 361275, 481899, 1354828, 6328548, 6679881, ... (OEIS A005849; Caldwell). As of Nov. 2015, it is known that there are no other Cullen primes for n<13705481 (PrimeGrid).

Associated person

James Cullen

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