PARI/gp – meditationatae

The cubic Frobenius primality test as a Pari/gp script

PARI/gp code related to RH criterion, Lagarias: sigma_1(n) asymptotics

The essential PARI/gp code to check my computation is below: ? primorial(1)%462 = 2? primorial(1)^6%463 = 64? m16%464 = m16? \uharmonic = (Z)->Euler+psi(Z+1) primorial = (W)->prod(X=1,W,prime(X)) ? Qr(W) = sigma(W,1)/(harmonic(W)+log(harmonic(W))*exp(harmonic(W)))%465 = (W)->sigma(W,1)/(harmonic(W)+log(harmonic(W))*exp(harmonic(W)))? m16%466 = m16? m16 = primorial(1614)*primorial(37)*primorial(11)*primorial(6)*primorial(4)*primorial(3)*primorial(2)^4*primorial(1)^6 ;? Qr(m16)%468 = 0.99923459761253613955435440267376833156?

Some Rabin-Miller pseudoprime primality tests

? 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)…