A Cullen number (first studied by Reverend James Cullen in 1905) is a number of the form n * 2^n + 1. A Woodall number (first studied by Allan Cunningham and H.J. Woodall in 1917) is a number of the form n * 2^n - 1.
Generalized Cullen and Woodall numbers are of the form n * b^n + 1 and n * b^n - 1, respectively, where n + 2 > b.
PrimeGrid is moving its search for Generalized Cullen and Generalized Woodall primes from PRPNet to BOINC. As is customary when projects move from PRPNet, PrimeGrid will double-check the ranges searched by PRPNet, and will then continue on with new work running multiple bases (b values) concurrently and incrementing through n values.
PrimeGrid will be sieving to a much larger n than has been previously done. The largest candidates will be in excess of 15,000,000 digits, and will be the same size as the largest candidates in the Seventeen or Bust project.
Once PrimeGrid finds a Generalized Cullen or Woodall on a base, it stops looking for Generalized Cullen or Woodall primes on that base, depending on the type found. For all the current bases, PrimeGrid has found a Generalized Woodall prime, and will initially be searching only for Generalized Cullen Primes.
The following bases have yet to produce a prime (highlighted ones have been found):
- Woodall b=43, 104 & 121
- Cullen b=13, 25, 29, 41, 47, 49, 53, 55, 68, 69, 73, 79, 101, 109, 113, 116 & 121
Base 149 is the next primeless base for both GC and GW.
Once the sieving has built a sufficient and sustainable pool of credits, PrimeGrid anticipates restarting LLR work as well, and would expect this to occur in early 2017.
In addition to having found the largest known Cullen prime http://primes.utm.edu/primes/page.php?id=89536 and largest known Woodall prime http://primes.utm.edu/primes/page.php?id=83407, PrimeGrid has found the largest known Generalized Cullen prime, http://primes.utm.edu/primes/page.php?id=124515 and the 4th largest known Generalized Woodall prime http://primes.utm.edu/primes/page.php?id=98862.
For more information on Generalized Cullen and Woodall Numbers, you can go here: http://primes.utm.edu/top20/page.php?id=42 and here: http://primes.utm.edu/top20/page.php?id=45.