Sieving primes up to 10000000...
  664578 primes, 1s
  power sums built, 8s
logG[1..8] (real, s=1):
  logG[1] = [-0.81571845 +/- 3.98e-9]
  logG[2] = [0.10112371 +/- 6.02e-9]
  logG[3] = [0.01658754643 +/- 3.15e-12]
  logG[4] = [0.003623284941 +/- 6.18e-14]
  logG[5] = [0.0009010034968 +/- 1.52e-14]
  logG[6] = [0.0002408478084 +/- 3.95e-14]
  logG[7] = [6.733326516e-5 +/- 1.95e-15]
  logG[8] = [1.939442081e-5 +/- 4.73e-15]
  Cauchy extraction done, 0s

Certified |c_i| * 2^i (i=1..20), P=10000000, prec=300 bits, N=2048 samples:
  i= 1: |c_i|=[0.8157184604 +/- 1.01e-11]   |c_i|*2^i=[1.6314369 +/- 2.09e-8]   rad=1.129e-08
  i= 2: |c_i|=[0.4338220125 +/- 4.43e-11]   |c_i|*2^i=[1.7352880 +/- 4.99e-8]   rad=1.124e-08
  i= 3: |c_i|=[0.1563636504 +/- 1.60e-11]   |c_i|*2^i=[1.2509092 +/- 3.33e-9]   rad=1.116e-08
  i= 4: |c_i|=[0.04729724119 +/- 4.86e-12]   |c_i|*2^i=[0.75675586 +/- 1.04e-9]   rad=1.116e-08
  i= 5: |c_i|=[0.01118691936 +/- 4.03e-12]   |c_i|*2^i=[0.35798142 +/- 3.52e-10]   rad=1.115e-08
  i= 6: |c_i|=[0.002494635551 +/- 3.02e-13]   |c_i|*2^i=[0.15965668 +/- 4.76e-9]   rad=1.115e-08
  i= 7: |c_i|=[0.0004233075665 +/- 5.36e-15]   |c_i|*2^i=[0.054183369 +/- 4.88e-10]   rad=1.115e-08
  i= 8: |c_i|=[8.398456478e-5 +/- 3.71e-15]   |c_i|*2^i=[0.021500049 +/- 4.16e-10]   rad=1.115e-08
  i= 9: |c_i|=[8.426007886e-6 +/- 3.17e-16]   |c_i|*2^i=[0.0043141160 +/- 3.75e-11]   rad=1.115e-08
  i=10: |c_i|=[2.577151162e-6 +/- 7.58e-17]   |c_i|*2^i=[0.0026390028 +/- 1.01e-11]   rad=1.115e-08
  i=11: |c_i|=[1.376935684e-7 +/- 3.54e-17]   |c_i|*2^i=[0.00028199643 +/- 1.85e-12]   rad=1.115e-08
  i=12: |c_i|=[1.450090161e-7 +/- 6.79e-18]   |c_i|*2^i=[0.00059395693 +/- 8.24e-14]   rad=1.115e-08
  i=13: |c_i|=[4.502030008e-8 +/- 1.66e-18]   |c_i|*2^i=[0.00036880630 +/- 1.74e-12]   rad=1.115e-08
  i=14: |c_i|=[2.362059410e-8 +/- 4.81e-18]   |c_i|*2^i=[0.00038699981 +/- 3.66e-12]   rad=1.115e-08
  i=15: |c_i|=[1.518197812e-8 +/- 2.10e-18]   |c_i|*2^i=[0.00049748306 +/- 1.04e-12]   rad=1.115e-08
  i=16: |c_i|=[1.250190871e-8 +/- 4.01e-18]   |c_i|*2^i=[0.00081932509 +/- 5.20e-13]   rad=1.114e-08
  i=17: |c_i|=[1.159748320e-8 +/- 2.40e-18]   |c_i|*2^i=[0.0015201053 +/- 1.84e-11]   rad=1.115e-08
  i=18: |c_i|=[1.129729962e-8 +/- 7.20e-19]   |c_i|*2^i=[0.0029615193 +/- 1.18e-11]   rad=1.115e-08
  i=19: |c_i|=[1.119642141e-8 +/- 3.46e-18]   |c_i|*2^i=[0.0058701494 +/- 1.37e-11]   rad=1.115e-08
  i=20: |c_i|=[1.116323784e-8 +/- 9.03e-19]   |c_i|*2^i=[0.011705503 +/- 2.81e-10]   rad=1.115e-08

Head sum (i=1..20) of |c_i|*2^i: [5.999670509 +/- 3.34e-10]
Compare to the session's certified S* = 6.98 (head to i=14 + geometric tail).
If this head sum is noticeably BELOW 6.98 minus the old tail (~1e-8), the
extension genuinely tightened S*. If coefficients plateau or grow with i
well before i=IMAX, the precision floor has been hit again -- increase P further.

Total time: 9s