mersenneforum.org A new Wagstaff PRP test ?
 User Name Remember Me? Password
 Register FAQ Search Today's Posts Mark Forums Read

2023-01-10, 21:01   #23
T.Rex

Feb 2004
France

3·311 Posts

Quote:
 Originally Posted by kijinSeija 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.

2023-01-10, 21:10   #24
T.Rex

Feb 2004
France

3×311 Posts

Quote:
 Originally Posted by kijinSeija 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

 Thread Tools

 Similar Threads Thread Thread Starter Forum Replies Last Post paulunderwood Wagstaff PRP Search 10 2022-03-31 04:19 GP2 Wagstaff PRP Search 414 2020-12-27 08:11 Tony Reix Wagstaff PRP Search 7 2013-10-10 01:23 Batalov GMP-ECM 9 2012-08-24 10:26 ixfd64 Math 12 2010-01-05 16:36

All times are UTC. The time now is 17:11.

Mon Feb 6 17:11:01 UTC 2023 up 172 days, 14:39, 1 user, load averages: 0.84, 0.98, 1.03

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2023, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.

≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °
∠ ∟ ° ≅ ~ ‖ ⟂ ⫛
≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳
∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟
¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣ … ⋯ ⋮ ⋰ ⋱
∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ
𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎𝜍 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔