Primality proof for n = 19701003098197239606139520050071806902539869635232723333974146702122860885748605305707133127442457820403313995153221:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=34275585315876169535825731013955432020686980960977076060073381689104960386232837.html>34275585315876169535825731013955432020686980960977076060073381689104960386232837 is prime.</a>
<br>b^((n-1)/34275585315876169535825731013955432020686980960977076060073381689104960386232837)-1 mod n = 8090285113184243004787500653833530510357245637967401445148586129910198356940413079335043032256009824518036949790635, which is a unit, inverse 15926837294084265914512608077581901002830560249072567136617703451062400543486642225766005912133472089523441453955793.
<p>(34275585315876169535825731013955432020686980960977076060073381689104960386232837) divides n-1.
<p>(34275585315876169535825731013955432020686980960977076060073381689104960386232837)^2 > n.
<p>n is prime by Pocklington's theorem.