mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Miscellaneous Math

Reply
 
Thread Tools
Old 2022-09-23, 21:43   #12
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

22×29×37 Posts
Default

Quote:
Originally Posted by paulunderwood View Post
Taking the obvious case of r=1, then a Lucas test over y^2-4*y+5 can be transformed into a 5-Euler PRP test and a Euler-Lucas test over f(z)=z^2-6/5*z+1 (for gcd(5,n)==1). This has solutions of f(z)=0 for z=(3+-4*i)/5. The corresponding companion matrix is Z=[3/5,-4/5;1,0], the determinant of which is 4/5. Thus if n is base 2-Fermat PRP there is no need to do the base 5-Euler PRP test -- it is implied since det(Z)^k == det(Z^k) for all k.
My logic is flawed that base 2 Fermat PRPs can replace base 5 Euler PRPs. I mistakenly wrote the wrong matrix Z; It should be [3/5,-4/5;4/5,3/5] (the determinant of which is 1). No more over egging the pudding.
paulunderwood is online now   Reply With Quote
Old 2022-09-24, 10:59   #13
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

22·29·37 Posts
Default

Quote:
Originally Posted by paulunderwood View Post
I'll call it day after verification to 10^15 of the test:

n==3 mod 4
2^n==2 mod n
(I+2^r)^n==-I+2^r mod n where I is the sqrt(-1)
gcd(r,n-1)==1
FWIW testing has reached 10^15
paulunderwood is online now   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Sigma parameter in ecm storm5510 Information & Answers 4 2019-11-30 21:32
PrimeNet error 7: Invalid parameter ksteczk PrimeNet 6 2018-03-26 15:11
changing mprime's WorkerThreads parameter? ozturkfa Information & Answers 7 2012-04-03 16:19
Parameter Underestimation R.D. Silverman Cunningham Tables 14 2010-09-29 19:56
ECM Work and Parameter Choices R.D. Silverman Cunningham Tables 11 2006-03-06 18:46

All times are UTC. The time now is 07:56.


Tue Oct 4 07:56:11 UTC 2022 up 47 days, 5:24, 0 users, load averages: 0.86, 1.31, 1.21

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2022, 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