High Quality Content by WIKIPEDIA articles! In number theory, a Woodall number is a natural number of the form n x 2n ? 1 (written Wn). Woodall numbers were first studied by Allan J. C. Cunningham and H. J. Woodall in 1917, inspired by James Cullen's earlier study of the similarly-defined Cullen numbers. The first few Woodall numbers are 1, 7, 23, 63, 159, 383, 895, … (sequence A003261 in OEIS). Woodall numbers curiously arise in Goodstein's theorem. It is conjectured that almost all Woodall numbers are composite; a proof has been submitted by H. Suyama, but it has not been verified yet. Nonetheless, it is also conjectured that there are infinitely many Woodall primes. As of December 2007, the largest known Woodall prime is 3752948 x 23752948 ? 1. It has 1,129,757 digits and was found by Matthew J. Thompson in 2007 in the distributed computing project PrimeGrid.

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