| Woodall Number |
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Woodall numbers curiously arise in Goodstein's Theorem . Woodall numbers that are also Prime Number s are called Woodall primes; the first few exponents ''n'' for which the corresponding Woodall numbers ''W''''n'' are prime are 2, 3, 6, 30, 75, 81, 115, 123, 249, 362, 384, ... ; the Woodall primes themselves begin with 7, 23, 383, 32212254719, ... . Like Cullen Number s, Woodall numbers have many divisibility properties. For example, if ''p'' is a prime number, then ''p'' divides W W It is conjectured that Almost All Woodall numbers are Composite ; a Proof has been submitted by Suyama , but it has not been verified yet. Nonetheless, it is also conjectured that there are infinitely many Woodall primes. A generalized Woodall number is defined to be a number of the form ''n'' · ''b''''n'' − 1, where ''n'' + 2 > ''b''; if a prime can be written in this form, it is then called a '''generalized Woodall prime'''. EXTERNAL LINKS |