Woodall numbers: W(n) = n·2^n − 1. W(1)=1, W(2)=7, W(3)=23, W(4)=63, W(5)=159... Woodall primes: 7,23,W(6)=383,W(30),W(75),W(81)... Named after H.J. Woodall who studied them in early 1900s. Related to Cullen numbers C(n)=n·2^n+1.
How to Use
Enter n:
- W(n): Woodall number value
- Prime?: Primality test
- Sequence: First several W(n)
Woodall Primes
No simple pattern for which n give prime W(n). Known indices: 2,3,6,30,75,81,115,123,249,362,384,515,1023... Tested using special sieving and LLR (Lucas-Lehmer-Riesel) test. The largest known has millions of digits.
Cullen Relation
Cullen: C(n)=n·2^n+1. Woodall: W(n)=n·2^n−1. They differ by 2. If both C(n) and W(n) are prime, they form a 'Cullen-Woodall twin'. This is extremely rare — n=3 gives C(3)=25 (not prime), W(3)=23 (prime).
Step-by-Step Instructions
- 1Enter n.
- 2Compute W(n).
- 3Test primality.
- 4Generate sequence.
- 5Compare to Cullen.