May 2013 – meditationatae

Pseudoprimes from iterating f(x)=4x+1 starting with x=3

? count=0;for(W=1,5555130,for(Z=W,W, par=W;new=3; for(X=1,par,new=4*new+1);if( ispseudoprime(new,1) ,count=count+1; print(W,” “,count,” “,round(log(new)/log(10)) ) )) )1 1 12 2 24 3 35 4 48 5 510 6 711 7 720 8 1332 9 2040 10 25131 11 79257 12 155263 13 159350 14 211448 15 270634 16 382725 17 437803 18 484832 19 5011769 20 10662363 21 14232548 22… Continue reading Pseudoprimes from iterating f(x)=4x+1 starting with x=3

Some Rabin-Miller pseudoprime primality tests (updated)

? m=55;s=m;for(X=1,6,s=s^4-s^2+1);print(m,” “,round(log(s)/log(10)))55 7128 ? ispseudoprime(s,30)%39 = 1 ? m=1948;s=m;for(X=1,6,s=s^4-s^2+1);print(m,” “,round(log(s)/log(10)))1948 13474 ? ispseudoprime(s,30)%40 = 1 ? m=3269;s=m;for(X=1,6,s=s^4-s^2+1);print(m,” “,round(log(s)/log(10)))3269 14395 ? ispseudoprime(s,30)%41 = 1 ? m=3981;s=m;for(X=1,6,s=s^4-s^2+1);print(m,” “,round(log(s)/log(10)))3981 14746 ? ispseudoprime(s,30)%42 = 1

Some Rabin-Miller pseudoprime primality tests

“best of 94” sample 13-character passwords

Some researchers a Georgia Tech. recommened 12-character passwords as good enough for most people and most uses. This is from the 95 printable ASCII characters. One of these 95 is Space or Space Bar, and there are suggestions that Space might be problematic on some systems for login. So, pesonally, I exclude Space, which leaves… Continue reading “best of 94” sample 13-character passwords

found old Königsberg on the map …

Königsberg was the capital city of the Kingdom of Prussia until about 1701, when the Prussian capital changed to Berlin. Aside: the Seven Bridges of Königsberg problem was solved by Swiss mathematician Euler in 1735, which is regarded as the first “result” or first paper in graph theory. Königsberg was almost destroyed in 1945. It now has the name Kaliningrad, and although part of Russia, is not connected to Russia (an exclave).

Essai de Lamia EL-SAAD sur Napoléon, d’Emil Ludwig

Lamia EL-SAAD, ecrivant sur le site Web de L’Orient Littéraire, passe en revue brievement plusieurs bibliographies de Napoléon, en mettant en relief le portrait psychologique et l’origine Corse de Napoleon et autres “speciaux” du livre d’Emil Ludwig avec ce qu’on retrouve dans grand nombres d’autres bibliographies de merite. Dans son essai, Lamia EL-SAAD conclue par: “Un incontournable pour les esprits napoléoniens, un délice pour les esprits curieux…” Essai publie en septembre 2012. Reimpression d’une traduction en francais de l’original en allemand chez Payot dans sa collection “Histoire Payot”, cf.: http://www.payot-rivages.net/livre_Napoleon-Emil-Ludwig_ean13_9782228907729.html

fickle fashion has veered to velvet

“fickle fashion has veered to velvet” is a newspaper citation occuring in the book Propaganda, by Edward L. Bernays, published in 1928. Bernays also writes that Emil Ludwig (?) represented Napoleon as a man always attententive to the voice/voices of public opinion.

Detexify online resource

I tried it myself and thought it was good:

http://detexify.kirelabs.org/classify.html

It’s an online program that takes a symbol drawn with the mouse and gives some guesses for the Latex code of the symbol. The people at AMS blog that commented gave positive reviews or comments.

finding irregular primes below a limit with PARI/gp

Irregular primes were defined/known by Kummer, around 1850. Kummer studied cyclotomic extensions of Q and, I think, their ring of integers (in modern parlance). The series of commands below has PARI/gp find the irregular primes (the number of them) below 125,000; this and more was done in a paper of Wagstaff in 1978. He found:… Continue reading finding irregular primes below a limit with PARI/gp

Where to start with Mochizuki’s work?

I’ve been searching a lot on the Web to get seemingly relevant background material on the works of S. Mochizuki. One promising article/preprint is entitled: The Grothendieck Conjecture on the Fundamental Groups of Algebraic Curves. The authors are: Hiroaki Nakamura , Akio Tamagawa and Shinichi Mochizuki .

rho_1 of zeta to 89000d (preliminary)

14.1347251417 3469379045 7251983562 4702707842 5711569924 3175685567 4601499634 2980925676 4949010393 1715610127 7920297154 8797436766 1426914698 8225458250 5363239447 1377804133 8123720597 0549621955 8658602005 5556672583 6010773700 2054109826 6150754278 0517442591 3062544819 7865107230 4938725629 7383215774 2039521572 5674809332 1400349904 6803434626 7314420920 3773854871 4137831735 6396995365 4281130796 8053149168 8529067820 8229804926 4338666734 6233200787 5876179200 5604868054 3568014444 2465106559 7568665903 2286865105 4485944432 0624072727 0320942745 2221304874 8720924123 8514183514 6054279015… Continue reading rho_1 of zeta to 89000d (preliminary)

About the irregular primes p with 2<p<2000

Using PARI/gp , I find 121 irregular primes p such that 2< p < 2000. In AN APPLICATION OF HIGH-SPEED COMPUTING TO FERMAT’S LAST THEOREM,P.N.A.S., Jan. 1954, D.H. Lehmer, E. Lehmer and H. Vandiverfound using a computer 118 irregular primes between 2 and 2000.The authors also proved Fermat’s Last Theorem for the primesless than 2000,… Continue reading About the irregular primes p with 2<p<2000

irregular primes l with 2000< l < 2521

In Vandiver, H. S. “Examination of Methods of Attack on the Second Case of Fermat’s Last Theorem“, P.N.A.S. 1954 (vol 40), Vandiver found by computation that there are 26 irregular primes p such that 2000 < p < 2521. Computations I did with PARI/gp show the same. Below, `l’ and `2a’ are as in Vandiver’s… Continue reading irregular primes l with 2000< l < 2521

About irregular primes up to 4002

I’ve been using Kummer’s results relating irregular primes to divisibility properties of numerators of the even-index Bernoulli numbers to produce the odd irregular primes up to 4002. In the range 2520<= p <= 4002, I find 72 irregular primes, the same as in the ~August 1955 paper of Selfridge, Nicol and Vandiver in P.N.A.S. That… Continue reading About irregular primes up to 4002

Internationalization glossary (Penn State)

They have a glossary to do with characters, accents and so on as well as the relations with information technology.

BBC Horizon – The Secret You

This is a fascinating exploration into how conscious phenomenae relate to neural activity within the brain. Narrated by mathematician Marcus du Sautoy, who volunteers in several brain experiments.

Euler-Maclaurin formula for zeta in PARI/gp

for(X=1,khyber,t=t+bernfrac(2*X)*q;q = q*((s+2*X-1)*(s+2*X)/(N*N))/((2*X+1)*(2*X+2)) ); t = t + exp((1-s)*log(N))/(s-1) + exp(-s*log(N))/2 ; g = sum(X=1,N-1,exp(-s*log(X))); z2 = t+g; abs(z2)

Euler-MacLaurin computation of zeta

Using PARI/gp, this past February: We have a lower time of computation of 14 hours 26 min when, in the notation of H.M. Edwards’ in his book, N = 32,000 and ‘nu’ = 32,405 : ? N %682 = 32000 ? khyber %683 = 32405 ? t=0; q=s/(2*N*exp(s*log(N))); for(X=1,khyber,t=t+bernfrac(2*X)*q;\ q = q*((s+2*X-1)*(s+2*X)/(N*N))/((2*X+1)*(2*X+2)) );\ t =… Continue reading Euler-MacLaurin computation of zeta

Stanton Friedman Is Real

This is a short biographical movie on ufologist Stanton Friedman, directed by Paul Kimball, blogging at: The Other Side of Truth, http://redstarfilms.blogspot.ca/ . The short film features interviews with admirers and critics of Stanton Friedman’s talks, books and conclusions. Also, Friedman himself is interviewed.