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Message boards : Cullen/Woodall prime search : Welcome to the Cullen/Woodall Prime Search

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Reggie
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Joined: 10 May 14
Posts: 31
ID: 311759
Credit: 78,630,381
RAC: 808
Discovered 1 mega primeFound 1 prime in the 2018 Tour de PrimesFound 1 mega prime in the 2018 Tour de Primes321 LLR Gold: Earned 500,000 credits (501,251)Cullen LLR Gold: Earned 500,000 credits (507,205)ESP LLR Gold: Earned 500,000 credits (504,771)Generalized Cullen/Woodall LLR Gold: Earned 500,000 credits (500,544)PPS LLR Gold: Earned 500,000 credits (500,330)PSP LLR Gold: Earned 500,000 credits (530,606)SoB LLR Gold: Earned 500,000 credits (507,131)SR5 LLR Silver: Earned 100,000 credits (192,467)SGS LLR Gold: Earned 500,000 credits (500,037)TRP LLR Silver: Earned 100,000 credits (112,730)Woodall LLR Silver: Earned 100,000 credits (228,485)Generalized Cullen/Woodall Sieve Ruby: Earned 2,000,000 credits (2,000,420)PPS Sieve Sapphire: Earned 20,000,000 credits (20,579,955)AP 26/27 Jade: Earned 10,000,000 credits (10,976,745)GFN Sapphire: Earned 20,000,000 credits (20,412,818)PSA Sapphire: Earned 20,000,000 credits (20,070,245)
Message 116530 - Posted: 28 Mar 2018 | 15:59:24 UTC
Last modified: 1 Apr 2018 | 21:47:52 UTC

Welcome to the Cullen/Woodall Prime Search

A Cullen number 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.

Message boards : Cullen/Woodall prime search : Welcome to the Cullen/Woodall Prime Search

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