prob123(N)=
{
  default(primelimit,1000000);
  n = 1;
  first = 1;
  forprime(p=2,N,
    psquared = p^2;
    v = (p-1)^n + (p+1)^n;
    r = v % psquared;
    if ((r > 10^9 && first == 1),
      print1("10^9: ");
      print(n);
      first = 0;
    );
    if ((r > 10^10),
      print1("10^10: ");
      print(n);
      break;
    );
    n++;
  );
}