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Old 2023-01-10, 21:01   #23
T.Rex
 
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Quote:
Originally Posted by kijinSeija View Post
Let W_p = (2^p+1)/3 where p is a prime number >3

Let the sequence S_i = S_{i-1}^2-2 with S_0 = 1/4 = (2^{(p-2)}+1)/3

W_p is prime if S_{p-2} \equiv (W_p-1)/2+2 \equiv 2 \cdot S_0 + 1
2*S0+1 = 1/2+1 = 3/2 and (3/2)^2-2 = 1/4 .

Nothing new. Just start with 3/2.
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Old 2023-01-10, 21:10   #24
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Quote:
Originally Posted by kijinSeija View Post

Let  Np=2^p+1 and  Wp=(2^p+1)/3 for Wagstaff numbers with p a prime number > 3.

Then W_p is prime if S_{p-2} \equiv 10 \cdot S_0 - 1 (mod N_p) and p \equiv 2 (mod 3) or S_{p-2} \equiv 2 \cdot S_0 + 1 (mod N_p) and p \equiv 1 (mod 3)
Can't get what is S0.

Anyway, use modulo Np is a good idea.


About LLT good for N numbers such that N+1 can be easily factored, yes it is written in books. But that's wrong.
The LLT (with a different seed than 4 : 5) can be used for proving that a Fermat number is prime. There are at least 3 proofs for this, including mine.
See: PrimalityTest2FermatNumbers.pdf
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