Section: New Results

Search for Primitive Trinomials

Participant : Paul Zimmermann [contact] .

This is a joint work with Richard Brent (University of Newcastle, Australia).

We have performed a search for primitive trinomials $x^r+x^s+1$ over $GF\left(2\right)$ of degree $r=42643801$, $r=43112609$, $r=57885161$ and $r=74207281$, which are the new Mersenne prime exponents found by the GIMPS project. We found respectively 5, 4, 0 and 3 primitive trinomials [16], for example the three primitive trinomials of degree $74207281$ are (with their reverse trinomials):