Welcome to the Cullen/Woodall Prime Search

A Cullen number is in the form of n*2^n+1. Fr. James Cullen first studied these numbers in 1905 because they have interesting divisibility properties. It is conjectured that there are infinitely many n values that will yield Cullen primes, though it has been shown that almost all are composite.

Further reading:
Cullen Number on Wikipedia
Top Twenty Cullen Primes in Chris Caldwell's Database

The following n values yield prime Cullen numbers (OEIS A005849) (ones found at PrimeGrid highlighted):

1, 141, 4713, 5795, 6611, 18496, 32292, 32469, 59656, 90825, 262419, 361275, 481899, 1354828, 6328548, and 6679881.

A Woodall number is in the form n*2^n-1. They are named after Herbert J. Woodall in 1917, when he studied them and their divisibility properties after being inspired by Fr. James Cullen. They are also called Cullen numbers of the second kind. Similarly to Cullen numbers, it is conjectured that there are infinitely many n values that will yield Woodall primes, though it has been shown that almost all are composite.

Further reading:
Woodall Number on Wikipedia
Top Twenty Woodall Primes in Chris Caldwell's Database

The following n values yield prime Woodall numbers (OEIS A002234) (ones found at PrimeGrid highlighted):

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, 3752948, and 17016602.