Corrigenda to ``New primitive $t$-nomials $(t=3,5)$ over $GF(2)$ whose degree is a Mersenne exponent,'' and some new primitive pentanomials

We report an error in our previous paper [#!K1!#], where we announced that we listed all the primitive trinomials over $GF(2)$ of degree 859433, but there is a bug in the sieve. We missed the primitive trinomial $X^{859433}+X^{170340}+1$ and its reciprocal, as pointed out by Richard Brent et al. We also report some new primitive pentanomials.