p_0 mod 2^20 = 908568   p_1 mod 2^20 = 949579
lambda_0/2 mod 2^20 = 479207   lambda_1/2 mod 2^20 = 694063
lambda_0 and lambda_1 first differ modulo 2^4 (as units lambda_s/2)
tau'(p_0) = p_1 checked mod 2^70
difference quotients q(2^k) = (tau'(p_0+2^k) - p_1)/2^k, shown mod 8 (precision 2^(NN-k)):
  k=1..39: [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]
if tau' were differentiable at p_0 these residues would be eventually constant.
q_j mod 16 along x_j = h_0^j(1), j = 0..24: [7, 3, 3, 11, 3, 11, 3, 11, 3, 11, 3, 11, 3, 11, 3, 11, 3, 11, 3, 11, 3, 11, 3, 11, 3]
q_(j+1)/q_j mod 2^10 for j = 12..23: [377, 377, 377, 377, 377, 377, 377, 377, 377, 377, 377, 377]  ; lambda_1/lambda_0 mod 2^10 = 377
