mersenneforum.org > Math Chebyshev polynomials and higher order Lucas Lehmer algorithm by Kok Seng Chu
 Register FAQ Search Today's Posts Mark Forums Read

 2022-01-10, 11:51 #1 T.Rex     Feb 2004 France 92710 Posts Chebyshev polynomials and higher order Lucas Lehmer algorithm by Kok Seng Chu Hi, I've found this recent (2021, October 3rd) paper named "CHEBYSHEV POLYNOMIALS AND HIGHER ORDER LUCAS LEHMER ALGORITHM", by KOK SENG CHUA, based on previous work by Pedja Terzi´c, and talking about the necessity part. This looks very interesting to me, since it provides a search about generalized Mersennes and the LLT (x^2-2). However, I've not spent yet enough time to read it, and it's not easy for me to understand it. So, I'd like to get comments from true mathematicians. https://arxiv.org/pdf/2010.02677.pdf Regards
 2022-01-11, 21:40 #2 T.Rex     Feb 2004 France 32·103 Posts The formula for Wagstaff numbers seems OK. With Pari/gp . Code: t(q)={w=(2^q+1)/3;S0=4;print("w: ",w);S=S0;for(i=1,q-1,S=Mod(S^2-2,w));s1=lift(Mod(S-5-9,w));s2=lift(Mod(S-5+9,w));print(s1," ",s2)} ? t(11) w: 683 665 0 ? t(13) w: 2731 0 18 ? t(17) w: 43691 43673 0 ? t(19) w: 174763 0 18 ? t(23) w: 2796203 2796185 0 ? t(29) w: 178956971 Not prime 59834419 59834437 ? t(31) w: 715827883 0 18 ? t(37) w: 45812984491 Not prime 24875527143 24875527161 ? t(41) w: 733007751851 Not prime 634893124730 634893124748 ? t(43) w: 2932031007403 0 18 ? t(61) w: 768614336404564651 0 18
 2022-01-15, 14:44 #3 Dr Sardonicus     Feb 2017 Nowhere 10110100010012 Posts The sufficiency result (Lemma 2.1) requires a complete factorization of Q + 1 or Q - 1 in order to prove that Q is prime.

 Similar Threads Thread Thread Starter Forum Replies Last Post carpetpool Miscellaneous Math 2 2018-04-15 00:28 carpetpool Abstract Algebra & Algebraic Number Theory 0 2017-04-19 20:33 Mathsgirl Information & Answers 23 2014-12-10 16:25 storm5510 Math 22 2009-09-24 22:32 Dougal Information & Answers 9 2009-02-06 10:25

All times are UTC. The time now is 14:10.

Wed May 18 14:10:43 UTC 2022 up 34 days, 12:12, 1 user, load averages: 2.44, 2.60, 2.10