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Woodall Numbers (sometimes called Cullen numbers 'of the second kind') are positive integers of the form Wn = n*2^n-1, where n is also a positive integer greater than zero. Woodall numbers that are prime are called Woodall primes (or Cullen primes of the second kind).

The Woodall numbers Wn are primes for the following n:

2, 3, 6, 30, 75, 81, 115, 123, 249, 362, 384, 462, 512, 751, 822, 5312, 7755, 9531, 12379, 15822, 18885, 22971, 23005, 98726, 143018, 151023, 667071, 1195203, 1268979, 1467763, 2013992, 2367906, and 3752948 and composite for all other n less than 12819728.

It is conjectured that there are infinitely many such primes.  PrimeGrid has found the 3 largest Woodall primes:

3752948·23752948-1 : official announcement
2367906·22367906-1 : official announcement
2013992·22013992-1 : official announcement

For more information on Woodall numbers, please visit the following sites:

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