Woodall Primes

Introduction

Woodall primes are prime numbers of the form n*2^n-1, where n is a positive integer. They are similar to Mersenne primes which are of the form 2^n-1. They were first studied by John Woodall in 1967.

History

The first few Woodall primes are:

• 3
• 7
• 23
• 63
• 159
• 383
• 895
• 2047
• 4607
• 10239

It was not until 1999 that all Woodall primes up to the form n*2^n-1 where n=100,000 have been factored completely.

Uses

Woodall primes have no known practical applications or uses. They are mostly studied for their mathematical properties and research purposes.

Calculation

The calculation of Woodall primes can be done using a computer program. Here's an example Python code snippet that calculates and prints the first 10 Woodall primes:

for n in range(1, 11):
    woodall = n * 2**n - 1
    if is_prime(woodall):
        print(woodall)

Note that is_prime() is a function that checks if a number is prime.

Conclusion

Woodall primes are an interesting topic in number theory. Although they have no practical uses, they are still studied for their properties and their relation to other prime numbers.