Frontier Survey

For $n$ unit squares, $s (n)$ is the side of the smallest square that holds them without overlap. The table compares reported and verified bounds for $n$ up to 324. Of these, 81 have a proved optimum and 243 are open.

The best known packing and reported lower bound are the published values. The verified columns require an exact proof, algebraic replay, or rigorous certificate; external certificates must be replayed in full with their assumptions discharged. Finite-precision numerical checks do not count as verified bounds. ✓ same means the verified and reported values agree. Published proof, not read here and defect recorded identify limits of the verification.

The gap is the verified upper bound minus the verified lower bound. Polynomial roots appear as decimals, cut rather than rounded. Red marks bounds published or proved since 22 August 2026; Recent sorts recent verified bounds first. Records opens the case file. Open a row for its packing, sources, and verification evidence; click a column heading to sort or use the filters to narrow the rows.

n	Recent	Status	Best known packing	Verified upper	Reported lower	Verified lower	Gap	Records
1		provedO=R	1	✓ same	1	✓ same	0	n-001.md Record
2		provedO=	2	✓ same	2	✓ same	0	n-002.md Record
3		provedO=	2	✓ same	2	✓ same	0	n-003.md Record
4		provedO=R	2	✓ same	2	✓ same	0	n-004.md Record
5		provedO=R	$2 + \frac{1}{2} \sqrt{2}$ ≈ 2.70710678…Göbel 1979	✓ same	2.70710678…Göbel 1979	✓ same	0	n-005.md Record
6		provedO=	3Kearney, Shiu 2001	✓ same	3Kearney, Shiu 2002	✓ samepublished proof, not read here	0	n-006.md Record
7	corrects Nagamochi 2005	provedO=	3	✓ same	3El Moumni 1999	✓ same	0	n-007.md Record
8	corrects Nagamochi 2005	provedO=	3	✓ same	3El Moumni 1999	✓ same	0	n-008.md Record
9		provedO=R	3	✓ same	3	✓ same	0	n-009.md Record
10		provedO=	$3 + \frac{1}{2} \sqrt{2}$ ≈ 3.70710678…Göbel 1979	✓ same	3.70710678…Stromquist 2003	✓ samepublished proof, not read here	0	n-010.md Record
11		provedO=R	3.87708359…Trump 1979	✓ same	3.87708359…Ahmed 2026	✓ same	0	n-011.md Record
12		open (reported proved)=	4	✓ same	4jatloe, Gurevitch, ctjlewis, Ahmed 2026	$\frac{7943}{2000}$ = 3.9715	$\frac{57}{2000}$ = 0.0285	n-012.md Record
13		provedO=	4Bentz 2009	✓ same	4Bentz 2010	✓ same	0	n-013.md Record
14	corrects Nagamochi 2005	provedO=	4	✓ same	4Friedman 2009	✓ same	0	n-014.md Record
15	corrects Nagamochi 2005	provedO=	4	✓ same	4El Moumni 1999	✓ same	0	n-015.md Record
16		provedO=R	4	✓ same	4	✓ same	0	n-016.md Record
17		open (reported proved)=	4.67553009…Bidwell 1998	✓ same	4.67553009…Overbeck 2026	$\frac{18641771}{4000000}$ = 4.66044275	0.01508734…	n-017.md Record
18		open=	$\frac{7}{2} + \frac{1}{2} \sqrt{7}$ ≈ 4.82287565…Hämäläinen 1980	✓ same	$\frac{941}{200}$ = 4.705Hosono 2026	✓ same	$\frac{\sqrt{7}}{2} - \frac{241}{200}$ ≈ 0.11787565…	n-018.md Record
19		open=	$3 + \frac{4}{3} \sqrt{2}$ ≈ 4.88561808…Wainwright 1979	✓ same	$\frac{193}{40}$ = 4.825Hosono 2026	✓ same	$\frac{4 \sqrt{2}}{3} - \frac{73}{40}$ ≈ 0.06061808…	n-019.md Record
20		open=	5	✓ same	$\frac{981}{200}$ = 4.905Hosono 2026	✓ same	$\frac{19}{200}$ = 0.095	n-020.md Record
21		provedO=	5	✓ same	5Daniel 2026	✓ same	0	n-021.md Record
22		provedO=	5Bentz 2018	✓ same	5Bentz 2016	✓ samepublished proof, not read here	0	n-022.md Record
23	corrects Nagamochi 2005	provedO=	5Nagamochi 2005	✓ same	5Nagamochi 2005	✓ same	0	n-023.md Record
24	corrects Nagamochi 2005	provedO=	5Friedman 1999	✓ same	5Friedman 1999	✓ same	0	n-024.md Record
25		provedO=R	5	✓ same	5	✓ same	0	n-025.md Record
26		open=	$\frac{7}{2} + \frac{3}{2} \sqrt{2}$ ≈ 5.62132034…Friedman 1997	✓ same	$\frac{1109}{200}$ = 5.545Hosono 2026	✓ same	$\frac{3 \sqrt{2}}{2} - \frac{409}{200}$ ≈ 0.07632034…	n-026.md Record
27		open=	$5 + \frac{1}{2} \sqrt{2}$ ≈ 5.70710678…Göbel 1979	✓ same	$\frac{11287}{2000}$ = 5.6435Hosono 2026	✓ same	$\frac{\sqrt{2}}{2} - \frac{1287}{2000}$ ≈ 0.06360678…	n-027.md Record
28		open=R	5.82444461…Ellsworth 2025	✓ same	$\frac{1147}{200}$ = 5.735Hosono 2026	✓ same	0.08944461…	n-028.md Record
29		open=	5.93383346…Schadt 2025	✓ same	$\frac{581}{100}$ = 5.81Hosono 2026	✓ same	0.12383346…	n-029.md Record
30		open=	6	✓ same	$\frac{11767}{2000}$ = 5.8835Hosono 2026	✓ same	$\frac{233}{2000}$ = 0.1165	n-030.md Record
31		open=	6	✓ same	$\frac{2391}{400}$ = 5.9775Hosono 2026	✓ same	$\frac{9}{400}$ = 0.0225	n-031.md Record
32		provedO=	6	✓ same	6Daniel 2026	✓ same	0	n-032.md Record
33		provedO=	6Bentz 2018	✓ same	6Bentz 2016	✓ same	0	n-033.md Record
34	corrects Nagamochi 2005	provedO=	6Nagamochi 2005	✓ same	6Nagamochi 2005	✓ same	0	n-034.md Record
35	corrects Nagamochi 2005	provedO=	6Friedman 1999	✓ same	6Friedman 1999	✓ same	0	n-035.md Record
36		provedO=R	6	✓ same	6	✓ same	0	n-036.md Record
37		open=	6.59861960…Cantrell 2002	✓ same	$\frac{2599}{400}$ = 6.4975Hosono 2026	✓ same	0.10111960…	n-037.md Record
38		open=	$6 + \frac{1}{2} \sqrt{2}$ ≈ 6.70710678…Göbel 1979	✓ same	$\frac{1309}{200}$ = 6.545Hosono 2026	✓ same	$\frac{\sqrt{2}}{2} - \frac{109}{200}$ ≈ 0.16210678…	n-038.md Record
39		open=	6.81072208…Schadt 2026	✓ same	$\frac{133}{20}$ = 6.65Hosono 2026	✓ same	0.16072208…	n-039.md Record
40		open=R	$4 + 2 \sqrt{2}$ ≈ 6.82842712…Göbel 1979	✓ same	$\frac{3359}{500}$ = 6.718Guzhou0806 2026	✓ same	$2 \sqrt{2} - \frac{1359}{500}$ ≈ 0.11042712…	n-040.md Record
41		open=	6.92669309…Schadt 2025	✓ same	$\frac{271}{40}$ = 6.775Hosono 2026	✓ same	0.15169309…	n-041.md Record
42		open=	7	✓ same	$\frac{2739}{400}$ = 6.8475Hosono 2026	✓ same	$\frac{61}{400}$ = 0.1525	n-042.md Record
43		open=	7	✓ same	$\frac{2763}{400}$ = 6.9075Hosono 2026	✓ same	$\frac{37}{400}$ = 0.0925	n-043.md Record
44		provedO=	7	✓ same	7Khalili, Gharabaghi 2026	✓ same	0	n-044.md Record
45		provedO=	7	✓ same	7Daniel 2026	✓ same	0	n-045.md Record
46		provedO=	7Bentz 2009	✓ same	7Bentz 2010	✓ same	0	n-046.md Record
47	corrects Nagamochi 2005	provedO=	7	✓ same	7Nagamochi 2005	✓ same	0	n-047.md Record
48	corrects Nagamochi 2005	provedO=	7	✓ same	7Nagamochi 2005	✓ same	0	n-048.md Record
49		provedO=R	7	✓ same	7	✓ same	0	n-049.md Record
50		open=	$7 + \frac{4}{7}$ ≈ 7.57142857…Schadt 2025	7.57142857…	$\frac{37}{5}$ = 7.4Hosono 2026	✓ same	0.17142857…	n-050.md Record
51		open=	$\frac{16 + 5 \sqrt{2}}{3}$ ≈ 7.69035593…Xu 2026	✓ same	$\frac{747}{100}$ = 7.47Hosono 2026	✓ same	$\frac{5 \sqrt{2}}{3} - \frac{641}{300}$ ≈ 0.22035593…	n-051.md Record
52		open=	$7 + \frac{1}{2} \sqrt{2}$ ≈ 7.70710678…Göbel 1979	✓ same	$\frac{151}{20}$ = 7.55Hosono 2026	✓ same	$\frac{\sqrt{2}}{2} - \frac{11}{20}$ ≈ 0.15710678…	n-052.md Record
53		open=	$\frac{13}{2} + \frac{1}{2} \sqrt{7}$ ≈ 7.82287565…Cantrell 2002	7.82287565…	$\frac{3051}{400}$ = 7.6275Hosono 2026	✓ same	0.19537565…	n-053.md Record
54		open=	$7 - \frac{1}{2} \sqrt{2} + \sqrt{1 + \sqrt{2}}$ ≈ 7.84666719…Cantrell 2005	7.84666719…	$\frac{1537}{200}$ = 7.685Hosono 2026	✓ same	0.16166719…	n-054.md Record
55		open≈	7.94577100…Schadt 2026	✓ same	$\frac{966}{125}$ = 7.728Hosono 2026	✓ same	0.21777100…	n-055.md Record
56		open=	8	✓ same	$\frac{3121}{400}$ = 7.8025Hosono 2026	✓ same	$\frac{79}{400}$ = 0.1975	n-056.md Record
57		open=	8	✓ same	$\frac{3149}{400}$ = 7.8725Hosono 2026	✓ same	$\frac{51}{400}$ = 0.1275	n-057.md Record
58		open=	8	✓ same	$\frac{1587}{200}$ = 7.935Hosono 2026	✓ same	$\frac{13}{200}$ = 0.065	n-058.md Record
59		provedO=	8	✓ same	8Hosono 2026	✓ same	0	n-059.md Record
60		provedO=	8	✓ same	8Daniel 2026	✓ same	0	n-060.md Record
61		provedO=	8	✓ same	8Daniel 2026	✓ same	0	n-061.md Record
62	corrects Nagamochi 2005	provedO=	8	✓ same	8Nagamochi 2005	✓ same	0	n-062.md Record
63	corrects Nagamochi 2005	provedO=	8	✓ same	8Nagamochi 2005	✓ same	0	n-063.md Record
64		provedO=R	8	✓ same	8	✓ same	0	n-064.md Record
65		open=	$5 + \frac{5}{2} \sqrt{2}$ ≈ 8.53553390…Göbel 1979	✓ same	$\frac{167}{20}$ = 8.35Hosono 2026	✓ same	$\frac{5 \sqrt{2}}{2} - \frac{67}{20}$ ≈ 0.18553390…	n-065.md Record
66		open=	$3 + 4 \sqrt{2}$ ≈ 8.65685424…Stenlund 1980	✓ same	$\frac{843}{100}$ = 8.43Hosono 2026	✓ same	$4 \sqrt{2} - \frac{543}{100}$ ≈ 0.22685424…	n-066.md Record
67		open=	$8 + \frac{1}{2} \sqrt{2}$ ≈ 8.70710678…Stenlund 1980	✓ same	$\frac{212}{25}$ = 8.48Hosono 2026	✓ same	$\frac{\sqrt{2}}{2} - \frac{12}{25}$ ≈ 0.22710678…	n-067.md Record
68		open=	8.79879523…Couzo 2026	✓ same	$\frac{853}{100}$ = 8.53Hosono 2026	✓ same	0.26879523…	n-068.md Record
69		open=	8.82719465…Morandi 2010	✓ same	$\frac{431}{50}$ = 8.62Hosono 2026	✓ same	0.20719465…	n-069.md Record
70		open=	8.88096037…Xu 2026	✓ same	$\frac{3463}{400}$ = 8.6575Hosono 2026	✓ same	0.22346037…	n-070.md Record
71		open≈	8.94407155…Schadt 2025	✓ same	$\frac{8721}{1000}$ = 8.721Hosono 2026	✓ same	0.22307155…	n-071.md Record
72		open=	9	✓ same	$\frac{219}{25}$ = 8.76Hosono 2026	✓ same	$\frac{6}{25}$ = 0.24	n-072.md Record
73		open=	9	✓ same	$\frac{8813}{1000}$ = 8.813Hosono 2026	✓ same	$\frac{187}{1000}$ = 0.187	n-073.md Record
74		open=	9	✓ same	$\frac{3547}{400}$ = 8.8675Hosono 2026	✓ same	$\frac{53}{400}$ = 0.1325	n-074.md Record
75		open=	9	✓ same	$\frac{447}{50}$ = 8.94Hosono 2026	✓ same	$\frac{3}{50}$ = 0.06	n-075.md Record
76		provedO=	9	✓ same	9Greff 2026	✓ same	0	n-076.md Record
77		provedO=	9	✓ same	9Hosono 2026	✓ same	0	n-077.md Record
78		provedO=	9	✓ same	9Daniel 2026	✓ same	0	n-078.md Record
79	corrects Nagamochi 2005	provedO=	9	✓ same	9Nagamochi 2005	✓ same	0	n-079.md Record
80	corrects Nagamochi 2005	provedO=	9	✓ same	9Nagamochi 2005	✓ same	0	n-080.md Record
81		provedO=R	9	✓ same	9	✓ same	0	n-081.md Record
82		open=	$6 + \frac{5}{2} \sqrt{2}$ ≈ 9.53553390…Göbel 1979	✓ same	$\frac{233}{25}$ = 9.32Hosono 2026	✓ same	$\frac{5 \sqrt{2}}{2} - \frac{83}{25}$ ≈ 0.21553390…	n-082.md Record
83		open=	9.63475764…Hajba 2024	✓ same	$\frac{937}{100}$ = 9.37Hosono 2026	✓ same	0.26475764…	n-083.md Record
84		open=	9.69793479…Xu 2026	✓ same	$\frac{3769}{400}$ = 9.4225Hosono 2026	✓ same	0.27543479…	n-084.md Record
85		open=	$\frac{11}{2} + 3 \sqrt{2}$ ≈ 9.74264068…Friedman 1997	✓ same	$\frac{379}{40}$ = 9.475Hosono 2026	✓ same	$3 \sqrt{2} - \frac{159}{40}$ ≈ 0.26764068…	n-085.md Record
86		open=	9.82053540…Xu 2026	✓ same	$\frac{9503}{1000}$ = 9.503Hosono 2026	✓ same	0.31753540…	n-086.md Record
87		open=	9.83881526…Ellsworth 2024	✓ same	$\frac{479}{50}$ = 9.58Hosono 2026	✓ same	0.25881526…	n-087.md Record
88		open=	9.88245103…Chaoweeraprasit 2026	✓ same	$\frac{481}{50}$ = 9.62Hosono 2026	✓ same	0.26245103…	n-088.md Record
89		open=	$5 + \frac{7}{2} \sqrt{2}$ ≈ 9.94974746…Stenlund 1980	✓ same	$\frac{193}{20}$ = 9.65Hosono 2026	✓ same	$\frac{7 \sqrt{2}}{2} - \frac{93}{20}$ ≈ 0.29974746…	n-089.md Record
90		open=	10	✓ same	$\frac{973}{100}$ = 9.73Hosono 2026	✓ same	$\frac{27}{100}$ = 0.27	n-090.md Record
91		open=	10	✓ same	$\frac{781}{80}$ = 9.7625Hosono 2026	✓ same	$\frac{19}{80}$ = 0.2375	n-091.md Record
92		open=	10	✓ same	$\frac{977}{100}$ = 9.77Hosono 2026	✓ same	$\frac{23}{100}$ = 0.23	n-092.md Record
93		open=	10	✓ same	$\frac{247}{25}$ = 9.88Hosono 2026	✓ same	$\frac{3}{25}$ = 0.12	n-093.md Record
94		open=	10	✓ same	$\frac{199}{20}$ = 9.95Hosono 2026	✓ same	$\frac{1}{20}$ = 0.05	n-094.md Record
95		provedO=	10	✓ same	10Greff 2026	✓ same	0	n-095.md Record
96		provedO=	10	✓ same	10Daniel 2026	✓ same	0	n-096.md Record
97		provedO=	10	✓ same	10Daniel 2026	✓ same	0	n-097.md Record
98	corrects Nagamochi 2005	provedO=	10	✓ same	10Nagamochi 2005	✓ same	0	n-098.md Record
99	corrects Nagamochi 2005	provedO=	10	✓ same	10Nagamochi 2005	✓ same	0	n-099.md Record
100		provedO=R	10	✓ same	10	✓ same	0	n-100.md Record
101		open=	$7 + \frac{5}{2} \sqrt{2}$ ≈ 10.53553390…	10.53553390…	$\frac{257}{25}$ = 10.28Hosono 2026	✓ same	0.25553390…	n-101.md Record
102		open=	10.60582869…Xu 2026	✓ same	$\frac{257}{25}$ = 10.28Hosono 2026	✓ same	0.32582869…	n-102.md Record
103		open=	10.67923204…Xu 2026	✓ same	$\frac{257}{25}$ = 10.28Hosono 2026	✓ same	0.39923204…	n-103.md Record
104		open=	$10 + \frac{1}{2} \sqrt{2}$ ≈ 10.70710678…	10.70710678…	10.28852785…Hosono 2026	$\frac{257}{25}$ = 10.28	0.42710678…	n-104.md Record
105		open=	10.78930378…Xu 2026	✓ same	10.35476005…Hosono 2026	$\frac{257}{25}$ = 10.28	0.50930378…	n-105.md Record
106	corrects Nagamochi 2005	open≈	10.82290804…Couzo 2026	✓ same	10.40397664…Hosono 2026	10.31070843…	0.51219960…	n-106.md Record
107	corrects Nagamochi 2005	open=	$10 - \frac{1}{2} \sqrt{2} + \sqrt{1 + \sqrt{2}}$ ≈ 10.84666719…Hajba 2024	10.84666719…	10.43679039…Hosono 2026	10.36154146…	0.48512573…	n-107.md Record
108		open=	10.90482101…Xu 2026	✓ same	$\frac{531}{50}$ = 10.62Hosono 2026	✓ same	0.28482101…	n-108.md Record
109	corrects Nagamochi 2005	open=	$6 + \frac{7}{2} \sqrt{2}$ ≈ 10.94974746…	10.94974746…	10.55129036…Hosono 2026	10.46242942…	0.48731804…	n-109.md Record
110	corrects Nagamochi 2005	open=	10.99678339…Couzo 2026	✓ same	10.60000000…Hosono 2026	10.51249219…	0.48429119…	n-110.md Record
111	corrects Nagamochi 2005	open=	11	✓ same	10.65400247…Hosono 2026	10.56230589…	$\frac{21}{2} - \frac{9 \sqrt{5}}{2}$ ≈ 0.43769410…	n-111.md Record
112	corrects Nagamochi 2005	open=	11	✓ same	10.71173419…Hosono 2026	10.61187420…	$\frac{21}{2} - \frac{\sqrt{409}}{2}$ ≈ 0.38812579…	n-112.md Record
113	corrects Nagamochi 2005	open=	11	✓ same	10.76858884…Hosono 2026	10.66120071…	$\frac{21}{2} - \frac{\sqrt{413}}{2}$ ≈ 0.33879928…	n-113.md Record
114	corrects Nagamochi 2005	open=	11	✓ same	10.80000000…Hosono 2026	10.71028892…	$\frac{21}{2} - \frac{\sqrt{417}}{2}$ ≈ 0.28971107…	n-114.md Record
115	corrects Nagamochi 2005	open=	11	✓ same	10.85495712…Hosono 2026	10.75914226…	$\frac{21}{2} - \frac{\sqrt{421}}{2}$ ≈ 0.24085773…	n-115.md Record
116	corrects Nagamochi 2005	open=	11	✓ same	10.91128204…Hosono 2026	10.80776406…	$\frac{21}{2} - \frac{5 \sqrt{17}}{2}$ ≈ 0.19223593…	n-116.md Record
117	corrects Nagamochi 2005	open (reported proved)=	11	✓ same	11Daniel 2026	10.85615758…	$\frac{21}{2} - \frac{\sqrt{429}}{2}$ ≈ 0.14384241…	n-117.md Record
118		provedO=	11	✓ same	11Daniel 2026	✓ same	0	n-118.md Record
119	corrects Nagamochi 2005	provedO=	11	✓ same	11Nagamochi 2005	✓ same	0	n-119.md Record
120	corrects Nagamochi 2005	provedO=	11	✓ same	11Nagamochi 2005	✓ same	0	n-120.md Record
121		provedO=R	11	✓ same	11	✓ same	0	n-121.md Record
122	corrects Nagamochi 2005	open=	$8 + \frac{5}{2} \sqrt{2}$ ≈ 11.53553390…	11.53553390…	$\frac{5 \sqrt{22}}{61} + 2 \sqrt{2} + \frac{489}{61}$ ≈ 11.22928087…Green 2000defect recorded	11.04751155…	0.48802235…	n-122.md Record
123	corrects Nagamochi 2005	open=	11.59137814…Xu 2026	✓ same	$\frac{5 \sqrt{22}}{61} + 2 \sqrt{2} + \frac{489}{61}$ ≈ 11.22928087…Green 2000defect recorded	11.09481005…	0.49656809…	n-123.md Record
124	corrects Nagamochi 2005	open=	$6 + 4 \sqrt{2}$ ≈ 11.65685424…	11.65685424…	$\frac{5 \sqrt{22}}{61} + 2 \sqrt{2} + \frac{489}{61}$ ≈ 11.22928087…Green 2000defect recorded	11.14189832…	0.51495592…	n-124.md Record
125	corrects Nagamochi 2005	open=	$11 + \frac{1}{2} \sqrt{2}$ ≈ 11.70710678…	11.70710678…	$\frac{5 \sqrt{22}}{61} + 2 \sqrt{2} + \frac{489}{61}$ ≈ 11.22928087…Green 2000defect recorded	11.18877916…	0.51832761…	n-125.md Record
126	corrects Nagamochi 2005	open=	11.74264068…Xu 2026	✓ same	11.31332385…Hosono 2026	11.23545527…	0.50718541…	n-126.md Record
127	corrects Nagamochi 2005	open=	11.81087878…Xu 2026	✓ same	11.37166657…Hosono 2026	11.28192932…	0.52894946…	n-127.md Record
128	corrects Nagamochi 2005	open=	11.82509196…Ellsworth 2024	✓ same	11.41019809…Hosono 2026	11.32820391…	0.49688805…	n-128.md Record
129	corrects Nagamochi 2005	open=	11.87001385…Ostashev 2026	✓ same	11.44220661…Hosono 2026	11.37428158…	0.49573226…	n-129.md Record
130	corrects Nagamochi 2005	open=	11.90243064…Couzo 2026	✓ same	11.48554056…Hosono 2026	11.42016483…	0.48226581…	n-130.md Record
131	corrects Nagamochi 2005	open=	11.94965958…Chaoweeraprasit 2026	✓ same	11.54554473…Hosono 2026	11.46585609…	0.48380348…	n-131.md Record
132	corrects Nagamochi 2005	open=	11.98568019…Daniel 2026	✓ same	11.60000000…Hosono 2026	11.51135777…	0.47432242…	n-132.md Record
133	corrects Nagamochi 2005	open=	12	✓ same	11.63808766…Hosono 2026	11.55667219…	$\frac{23}{2} - \frac{\sqrt{489}}{2}$ ≈ 0.44332780…	n-133.md Record
134	corrects Nagamochi 2005	open=	12	✓ same	11.68956528…Hosono 2026	11.60180165…	$\frac{23}{2} - \frac{\sqrt{493}}{2}$ ≈ 0.39819834…	n-134.md Record
135	corrects Nagamochi 2005	open=	12	✓ same	11.74120722…Hosono 2026	11.64674840…	$\frac{23}{2} - \frac{\sqrt{497}}{2}$ ≈ 0.35325159…	n-135.md Record
136	corrects Nagamochi 2005	open=	12	✓ same	11.79211927…Hosono 2026	11.69151464…	$\frac{23}{2} - \frac{\sqrt{501}}{2}$ ≈ 0.30848535…	n-136.md Record
137	corrects Nagamochi 2005	open=	12	✓ same	11.81885066…Hosono 2026	11.73610252…	$\frac{23}{2} - \frac{\sqrt{505}}{2}$ ≈ 0.26389747…	n-137.md Record
138	corrects Nagamochi 2005	open=	12	✓ same	11.86967293…Hosono 2026	11.78051417…	$\frac{23}{2} - \frac{\sqrt{509}}{2}$ ≈ 0.21948582…	n-138.md Record
139	corrects Nagamochi 2005	open=	12	✓ same	11.92023468…Hosono 2026	11.82475165…	$\frac{23}{2} - \frac{3 \sqrt{57}}{2}$ ≈ 0.17524834…	n-139.md Record
140	corrects Nagamochi 2005	open (reported proved)=	12	✓ same	12Daniel 2026	11.86881700…	$\frac{23}{2} - \frac{\sqrt{517}}{2}$ ≈ 0.13118299…	n-140.md Record
141		provedO=	12	✓ same	12Daniel 2026	✓ same	0	n-141.md Record
142	corrects Nagamochi 2005	provedO=	12	✓ same	12Nagamochi 2005	✓ same	0	n-142.md Record
143	corrects Nagamochi 2005	provedO=	12	✓ same	12Nagamochi 2005	✓ same	0	n-143.md Record
144		provedO=R	12	✓ same	12	✓ same	0	n-144.md Record
145	corrects Nagamochi 2005	open=	$9 + \frac{5}{2} \sqrt{2}$ ≈ 12.53553390…	12.53553390…	$\frac{22 \sqrt{6}}{145} + 2 \sqrt{2} + \frac{1307}{145}$ ≈ 12.21386694…Green 2000defect recorded	12.04339638…	0.49213752…	n-145.md Record
146	corrects Nagamochi 2005	open=	12.58378219…Daniel 2026	✓ same	$\frac{22 \sqrt{6}}{145} + 2 \sqrt{2} + \frac{1307}{145}$ ≈ 12.21386694…Green 2000defect recorded	12.08663022…	0.49715196…	n-146.md Record
147	corrects Nagamochi 2005	open=	$7 + 4 \sqrt{2}$ ≈ 12.65685424…	12.65685424…	$\frac{22 \sqrt{6}}{145} + 2 \sqrt{2} + \frac{1307}{145}$ ≈ 12.21386694…Green 2000defect recorded	12.12970334…	0.52715089…	n-147.md Record
148	corrects Nagamochi 2005	open=	$7 + 4 \sqrt{2}$ ≈ 12.65685424…	12.65685424…	$\frac{22 \sqrt{6}}{145} + 2 \sqrt{2} + \frac{1307}{145}$ ≈ 12.21386694…Green 2000defect recorded	12.17261752…	0.48423671…	n-148.md Record
149	corrects Nagamochi 2005	open=	$12 + \frac{1}{2} \sqrt{2}$ ≈ 12.70710678…	12.70710678…	12.28042698…Hosono 2026	12.21537451…	0.49173226…	n-149.md Record
150	corrects Nagamochi 2005	open=	$5 + \frac{11}{2} \sqrt{2}$ ≈ 12.77817459…Ellsworth 2025	12.77817459…	12.33286976…Hosono 2026	12.25797601…	0.52019857…	n-150.md Record
151	corrects Nagamochi 2005	open=	$\frac{23}{2} + \frac{1}{2} \sqrt{7}$ ≈ 12.82287565…Ellsworth 2024	12.82287565…	12.38531699…Hosono 2026	12.30042372…	0.52245193…	n-151.md Record
152	corrects Nagamochi 2005	open≈	12.83071880…Couzo 2026	✓ same	12.41570458…Hosono 2026	12.34271928…	0.48799951…	n-152.md Record
153	corrects Nagamochi 2005	open=	12.87001385…PingYou Ltd 2026	✓ same	12.44683233…Hosono 2026	12.38486432…	0.48514952…	n-153.md Record
154	corrects Nagamochi 2005	open=	12.92110094…Daniel 2026	✓ same	12.48666925…Hosono 2026	12.42686044…	0.49424049…	n-154.md Record
155	corrects Nagamochi 2005	open=	12.95226094…Daniel 2026	✓ same	12.54095430…Hosono 2026	12.46870920…	0.48355174…	n-155.md Record
156	corrects Nagamochi 2005	open=	12.97916585…Ostashev 2026	✓ same	12.59123326…Hosono 2026	12.51041214…	0.46875370…	n-156.md Record
157	corrects Nagamochi 2005	open=	13	✓ same	12.62537907…Hosono 2026	12.55197079…	$\frac{25}{2} - \frac{\sqrt{581}}{2}$ ≈ 0.44802920…	n-157.md Record
158	corrects Nagamochi 2005	open=	13	✓ same	12.67171926…Hosono 2026	12.59338662…	$\frac{25}{2} - \frac{3 \sqrt{65}}{2}$ ≈ 0.40661337…	n-158.md Record
159	corrects Nagamochi 2005	open=	13	✓ same	12.71884053…Hosono 2026	12.63466109…	$\frac{25}{2} - \frac{\sqrt{589}}{2}$ ≈ 0.36533890…	n-159.md Record
160	corrects Nagamochi 2005	open=	13	✓ same	12.76515316…Hosono 2026	12.67579566…	$\frac{25}{2} - \frac{\sqrt{593}}{2}$ ≈ 0.32420433…	n-160.md Record
161	corrects Nagamochi 2005	open=	13	✓ same	12.80000000…Hosono 2026	12.71679172…	$\frac{25}{2} - \frac{\sqrt{597}}{2}$ ≈ 0.28320827…	n-161.md Record
162	corrects Nagamochi 2005	open=	13	✓ same	12.83559094…Hosono 2026	12.75765067…	$\frac{25}{2} - \frac{\sqrt{601}}{2}$ ≈ 0.24234932…	n-162.md Record
163	corrects Nagamochi 2005	open=	13	✓ same	12.88166297…Hosono 2026	12.79837387…	$\frac{25}{2} - \frac{11 \sqrt{5}}{2}$ ≈ 0.20162612…	n-163.md Record
164	corrects Nagamochi 2005	open=	13	✓ same	12.92754064…Hosono 2026	12.83896267…	$\frac{25}{2} - \frac{\sqrt{609}}{2}$ ≈ 0.16103732…	n-164.md Record
165	corrects Nagamochi 2005	open (reported proved)=	13	✓ same	13Daniel 2026	12.87941840…	$\frac{25}{2} - \frac{\sqrt{613}}{2}$ ≈ 0.12058159…	n-165.md Record
166		provedO=	13	✓ same	13Daniel 2026	✓ same	0	n-166.md Record
167	corrects Nagamochi 2005	provedO=	13	✓ same	13Nagamochi 2005	✓ same	0	n-167.md Record
168	corrects Nagamochi 2005	provedO=	13	✓ same	13Nagamochi 2005	✓ same	0	n-168.md Record
169		provedO=R	13	✓ same	13	✓ same	0	n-169.md Record
170	corrects Nagamochi 2005	open=	$10 + \frac{5}{2} \sqrt{2}$ ≈ 13.53553390…Hajba 2024	13.53553390…	$\frac{6 \sqrt{26}}{85} + 2 \sqrt{2} + \frac{851}{85}$ ≈ 13.20012261…Green 2000defect recorded	13.03993620…	0.49559770…	n-170.md Record
171	corrects Nagamochi 2005	open=	$13 + \frac{4}{7}$ ≈ 13.57142857…Ellsworth 2025	13.57142857…	$\frac{6 \sqrt{26}}{85} + 2 \sqrt{2} + \frac{851}{85}$ ≈ 13.20012261…Green 2000defect recorded	13.07974562…	0.49168294…	n-171.md Record
172	corrects Nagamochi 2005	open=	13.61793569…Daniel 2026	✓ same	$\frac{6 \sqrt{26}}{85} + 2 \sqrt{2} + \frac{851}{85}$ ≈ 13.20012261…Green 2000defect recorded	13.11942946…	0.49850623…	n-172.md Record
173	corrects Nagamochi 2005	open=	$8 + 4 \sqrt{2}$ ≈ 13.65685424…	13.65685424…	13.20589271…Hosono 2026	13.15898890…	0.49786534…	n-173.md Record
174	corrects Nagamochi 2005	open=	$13 + \frac{1}{2} \sqrt{2}$ ≈ 13.70710678…	13.70710678…	13.25370596…Hosono 2026	13.19842509…	0.50868168…	n-174.md Record
175	corrects Nagamochi 2005	open=	13.76417431…Ostashev 2026	✓ same	13.30130208…Hosono 2026	13.23773920…	0.52643511…	n-175.md Record
176	corrects Nagamochi 2005	open=	13.79587231…Ostashev 2026	✓ same	13.34868401…Hosono 2026	13.27693233…	0.51893997…	n-176.md Record
177	corrects Nagamochi 2005	open≈	13.82297973…Couzo 2026	✓ same	13.39683002…Hosono 2026	13.31600561…	0.50697411…	n-177.md Record
178	corrects Nagamochi 2005	open=	$13 - \frac{1}{2} \sqrt{2} + \sqrt{1 + \sqrt{2}}$ ≈ 13.84666719…	13.84666719…	13.42000000…Hosono 2026	13.35496013…	0.49170706…	n-178.md Record
179	corrects Nagamochi 2005	open=	13.88379549…Chaoweeraprasit 2026	✓ same	13.45078944…Hosono 2026	13.39379695…	0.48999853…	n-179.md Record
180	corrects Nagamochi 2005	open=	13.91699352…Chaoweeraprasit 2026	✓ same	13.48763441…Hosono 2026	13.43251715…	0.48447636…	n-180.md Record
181	corrects Nagamochi 2005	open=	13.95081953…Chaoweeraprasit 2026	✓ same	13.53720305…Hosono 2026	13.47112177…	0.47969775…	n-181.md Record
182	corrects Nagamochi 2005	open=	13.97091643…Daniel 2026	✓ same	13.58291323…Hosono 2026	13.50961183…	0.46130460…	n-182.md Record
183	corrects Nagamochi 2005	open=	13.99958017…Daniel 2026	✓ same	13.61383353…Hosono 2026	13.54798835…	0.45159182…	n-183.md Record
184	corrects Nagamochi 2005	open=	14	✓ same	13.65721411…Hosono 2026	13.58625232…	$\frac{27}{2} - \frac{\sqrt{685}}{2}$ ≈ 0.41374767…	n-184.md Record
185	corrects Nagamochi 2005	open=	14	✓ same	13.70023755…Hosono 2026	13.62440474…	$\frac{27}{2} - \frac{\sqrt{689}}{2}$ ≈ 0.37559525…	n-185.md Record
186	corrects Nagamochi 2005	open=	14	✓ same	13.74269800…Hosono 2026	13.66244658…	$\frac{27}{2} - \frac{3 \sqrt{77}}{2}$ ≈ 0.33755341…	n-186.md Record
187	corrects Nagamochi 2005	open=	14	✓ same	13.78500618…Hosono 2026	13.70037878…	$\frac{27}{2} - \frac{\sqrt{697}}{2}$ ≈ 0.29962121…	n-187.md Record
188	corrects Nagamochi 2005	open=	14	✓ same	13.80718794…Hosono 2026	13.73820229…	$\frac{27}{2} - \frac{\sqrt{701}}{2}$ ≈ 0.26179770…	n-188.md Record
189	corrects Nagamochi 2005	open=	14	✓ same	13.84948097…Hosono 2026	13.77591804…	$\frac{27}{2} - \frac{\sqrt{705}}{2}$ ≈ 0.22408195…	n-189.md Record
190	corrects Nagamochi 2005	open=	14	✓ same	13.89162350…Hosono 2026	13.81352695…	$\frac{27}{2} - \frac{\sqrt{709}}{2}$ ≈ 0.18647304…	n-190.md Record
191	corrects Nagamochi 2005	open=	14	✓ same	13.93361714…Hosono 2026	13.85102992…	$\frac{27}{2} - \frac{\sqrt{713}}{2}$ ≈ 0.14897007…	n-191.md Record
192	corrects Nagamochi 2005	open (reported proved)=	14	✓ same	14Daniel 2026	13.88842783…	$\frac{27}{2} - \frac{\sqrt{717}}{2}$ ≈ 0.11157216…	n-192.md Record
193		provedO=	14	✓ same	14Daniel 2026	✓ same	0	n-193.md Record
194	corrects Nagamochi 2005	provedO=	14	✓ same	14Nagamochi 2005	✓ same	0	n-194.md Record
195	corrects Nagamochi 2005	provedO=	14	✓ same	14Nagamochi 2005	✓ same	0	n-195.md Record
196		provedO=R	14	✓ same	14	✓ same	0	n-196.md Record
197	corrects Nagamochi 2005	open=	$11 + \frac{5}{2} \sqrt{2}$ ≈ 14.53553390…	14.53553390…	$\frac{26 \sqrt{7}}{197} + 2 \sqrt{2} + \frac{2169}{197}$ ≈ 14.18776486…Green 2000defect recorded	14.03698637…	0.49854753…	n-197.md Record
198	corrects Nagamochi 2005	open=	$14 + \frac{4}{7}$ ≈ 14.57142857…	14.57142857…	$\frac{26 \sqrt{7}}{197} + 2 \sqrt{2} + \frac{2169}{197}$ ≈ 14.18776486…Green 2000defect recorded	14.07387196…	0.49755661…	n-198.md Record
199	corrects Nagamochi 2005	open=	14.61757217…Chaoweeraprasit 2026	✓ same	$\frac{26 \sqrt{7}}{197} + 2 \sqrt{2} + \frac{2169}{197}$ ≈ 14.18776486…Green 2000defect recorded	14.11065758…	0.50691458…	n-199.md Record
200	corrects Nagamochi 2005	open=	$9 + 4 \sqrt{2}$ ≈ 14.65685424…	14.65685424…	$\frac{26 \sqrt{7}}{197} + 2 \sqrt{2} + \frac{2169}{197}$ ≈ 14.18776486…Green 2000defect recorded	14.14734406…	0.50951018…	n-200.md Record
201	corrects Nagamochi 2005	open=	$14 + \frac{1}{2} \sqrt{2}$ ≈ 14.70710678…	14.70710678…	14.23158725…Hosono 2026	14.18393218…	0.52317459…	n-201.md Record
202	corrects Nagamochi 2005	open=	$2 + 9 \sqrt{2}$ ≈ 14.72792206…	14.72792206…	14.27513779…Hosono 2026	14.22042273…	0.50749932…	n-202.md Record
203	corrects Nagamochi 2005	open=	$7 + \frac{11}{2} \sqrt{2}$ ≈ 14.77817459…Ellsworth 2024	14.77817459…	14.31852405…Hosono 2026	14.25681649…	0.52135810…	n-203.md Record
204	corrects Nagamochi 2005	open=	14.80762747…Daniel 2026	✓ same	14.36174789…Hosono 2026	14.29311422…	0.51451324…	n-204.md Record
205	corrects Nagamochi 2005	open=	14.82445114…Ellsworth 2024	✓ same	14.40000000…Hosono 2026	14.32931668…	0.49513446…	n-205.md Record
206	corrects Nagamochi 2005	open=	14.86015866…Couzo 2026	✓ same	14.42000000…Hosono 2026	14.36542462…	0.49473403…	n-206.md Record
207	corrects Nagamochi 2005	open=	14.88096037…PingYou Ltd 2026	✓ same	14.45408302…Hosono 2026	14.40143877…	0.47952159…	n-207.md Record
208	corrects Nagamochi 2005	open=	14.92451877…Chaoweeraprasit 2026	✓ same	14.48846920…Hosono 2026	14.43735986…	0.48715890…	n-208.md Record
209	corrects Nagamochi 2005	open=	14.94622322…Chaoweeraprasit 2026	✓ same	14.53408043…Hosono 2026	14.47318861…	0.47303461…	n-209.md Record
210	corrects Nagamochi 2005	open=	14.97300111…Couzo 2026	✓ same	14.57597945…Hosono 2026	14.50892572…	0.46407539…	n-210.md Record
211	corrects Nagamochi 2005	open=	14.99354962…Ostashev 2026	✓ same	14.60509269…Hosono 2026	14.54457190…	0.44897772…	n-211.md Record
212	corrects Nagamochi 2005	open=	15	✓ same	14.64474665…Hosono 2026	14.58012784…	$\frac{29}{2} - \frac{\sqrt{793}}{2}$ ≈ 0.41987215…	n-212.md Record
213	corrects Nagamochi 2005	open=	15	✓ same	14.68420454…Hosono 2026	14.61559421…	$\frac{29}{2} - \frac{\sqrt{797}}{2}$ ≈ 0.38440578…	n-213.md Record
214	corrects Nagamochi 2005	open=	15	✓ same	14.72371854…Hosono 2026	14.65097169…	$\frac{29}{2} - \frac{3 \sqrt{89}}{2}$ ≈ 0.34902830…	n-214.md Record
215	corrects Nagamochi 2005	open=	15	✓ same	14.76278883…Hosono 2026	14.68626095…	$\frac{29}{2} - \frac{\sqrt{805}}{2}$ ≈ 0.31373904…	n-215.md Record
216	corrects Nagamochi 2005	open=	15	✓ same	14.80000000…Hosono 2026	14.72146265…	$\frac{29}{2} - \frac{\sqrt{809}}{2}$ ≈ 0.27853734…	n-216.md Record
217	corrects Nagamochi 2005	open=	15	✓ same	14.82224120…Hosono 2026	14.75657742…	$\frac{29}{2} - \frac{\sqrt{813}}{2}$ ≈ 0.24342257…	n-217.md Record
218	corrects Nagamochi 2005	open=	15	✓ same	14.86119516…Hosono 2026	14.79160592…	$\frac{29}{2} - \frac{\sqrt{817}}{2}$ ≈ 0.20839407…	n-218.md Record
219	corrects Nagamochi 2005	open=	15	✓ same	14.90003145…Hosono 2026	14.82654878…	$\frac{29}{2} - \frac{\sqrt{821}}{2}$ ≈ 0.17345121…	n-219.md Record
220	corrects Nagamochi 2005	open=	15	✓ same	14.93875111…Hosono 2026	14.86140661…	$\frac{29}{2} - \frac{5 \sqrt{33}}{2}$ ≈ 0.13859338…	n-220.md Record
221	corrects Nagamochi 2005	open (reported proved)=	15	✓ same	15Daniel 2026	14.89618004…	$\frac{29}{2} - \frac{\sqrt{829}}{2}$ ≈ 0.10381995…	n-221.md Record
222		provedO=	15	✓ same	15Daniel 2026	✓ same	0	n-222.md Record
223	corrects Nagamochi 2005	provedO=	15	✓ same	15Nagamochi 2005	✓ same	0	n-223.md Record
224	corrects Nagamochi 2005	provedO=	15	✓ same	15Nagamochi 2005	✓ same	0	n-224.md Record
225		provedO=R	15	✓ same	15	✓ same	0	n-225.md Record
226	corrects Nagamochi 2005	open=	$12 + \frac{5}{2} \sqrt{2}$ ≈ 15.53553390…	15.53553390…	$\frac{7 \sqrt{30}}{113} + 2 \sqrt{2} + \frac{1357}{113}$ ≈ 15.17657384…Green 2000defect recorded	15.03444185…	0.50109205…	n-226.md Record
227	corrects Nagamochi 2005	open=	15.56362565…de Winter 2026	✓ same	$\frac{7 \sqrt{30}}{113} + 2 \sqrt{2} + \frac{1357}{113}$ ≈ 15.17657384…Green 2000defect recorded	15.06880228…	0.49482336…	n-227.md Record
228	corrects Nagamochi 2005	open=	15.60460147…Couzo 2026	✓ same	$\frac{7 \sqrt{30}}{113} + 2 \sqrt{2} + \frac{1357}{113}$ ≈ 15.17657384…Green 2000defect recorded	15.10308186…	0.50151960…	n-228.md Record
229	corrects Nagamochi 2005	open=	15.65016151…Daniel 2026	✓ same	$\frac{7 \sqrt{30}}{113} + 2 \sqrt{2} + \frac{1357}{113}$ ≈ 15.17657384…Green 2000defect recorded	15.13728116…	0.51288034…	n-229.md Record
230	corrects Nagamochi 2005	open=	$15 + \frac{28}{41}$ ≈ 15.68292682…Ellsworth 2025	15.68292682…	15.21298563…Hosono 2026	15.17140075…	0.51152607…	n-230.md Record
231	corrects Nagamochi 2005	open=	$15 + \frac{1}{2} \sqrt{2}$ ≈ 15.70710678…	15.70710678…	15.25311210…Hosono 2026	15.20544116…	0.50166561…	n-231.md Record
232	corrects Nagamochi 2005	open=	15.76166175…Alex Chilton 2026	✓ same	15.29310997…Hosono 2026	15.23940297…	0.52225878…	n-232.md Record
233	corrects Nagamochi 2005	open=	$8 + \frac{11}{2} \sqrt{2}$ ≈ 15.77817459…	15.77817459…	15.33298048…Hosono 2026	15.27328670…	0.50488789…	n-233.md Record
234	corrects Nagamochi 2005	open=	$\frac{29}{2} + \frac{1}{2} \sqrt{7}$ ≈ 15.82287565…Ellsworth 2024	15.82287565…	15.37272482…Hosono 2026	15.30709289…	0.51578276…	n-234.md Record
235	corrects Nagamochi 2005	open=	15.82660563…Ellsworth, Cantrell 2025	✓ same	15.40294636…Hosono 2026	15.34082207…	0.48578355…	n-235.md Record
236	corrects Nagamochi 2005	open=	15.86193439…Daniel 2026	✓ same	15.42473742…Hosono 2026	15.37447478…	0.48745960…	n-236.md Record
237	corrects Nagamochi 2005	open=	15.90260363…Chaoweeraprasit 2026	✓ same	15.45709095…Hosono 2026	15.40805151…	0.49455212…	n-237.md Record
238	corrects Nagamochi 2005	open=	15.92410678…Chaoweeraprasit 2026	✓ same	15.48919837…Hosono 2026	15.44155279…	0.48255398…	n-238.md Record
239	corrects Nagamochi 2005	open=	15.94844332…Chaoweeraprasit 2026	✓ same	15.53144083…Hosono 2026	15.47497913…	0.47346419…	n-239.md Record
240	corrects Nagamochi 2005	open=	15.96968533…Couzo 2026	✓ same	15.57011298…Hosono 2026	15.50833101…	0.46135431…	n-240.md Record
241	corrects Nagamochi 2005	open=	15.98711709…Ostashev 2026	✓ same	15.60000000…Hosono 2026	15.54160895…	0.44550813…	n-241.md Record
242	corrects Nagamochi 2005	open=	16	✓ same	15.63431332…Hosono 2026	15.57481343…	$\frac{31}{2} - \frac{3 \sqrt{101}}{2}$ ≈ 0.42518656…	n-242.md Record
243	corrects Nagamochi 2005	open=	16	✓ same	15.67062445…Hosono 2026	15.60794492…	$\frac{31}{2} - \frac{\sqrt{913}}{2}$ ≈ 0.39205507…	n-243.md Record
244	corrects Nagamochi 2005	open=	16	✓ same	15.70747149…Hosono 2026	15.64100392…	$\frac{31}{2} - \frac{\sqrt{917}}{2}$ ≈ 0.35899607…	n-244.md Record
245	corrects Nagamochi 2005	open=	16	✓ same	15.74375646…Hosono 2026	15.67399090…	$\frac{31}{2} - \frac{\sqrt{921}}{2}$ ≈ 0.32600909…	n-245.md Record
246	corrects Nagamochi 2005	open=	16	✓ same	15.77994627…Hosono 2026	15.70690632…	$\frac{31}{2} - \frac{5 \sqrt{37}}{2}$ ≈ 0.29309367…	n-246.md Record
247	corrects Nagamochi 2005	open=	16	✓ same	15.80000000…Hosono 2026	15.73975065…	$\frac{31}{2} - \frac{\sqrt{929}}{2}$ ≈ 0.26024934…	n-247.md Record
248	corrects Nagamochi 2005	open=	16	✓ same	15.83510119…Hosono 2026	15.77252434…	$\frac{31}{2} - \frac{\sqrt{933}}{2}$ ≈ 0.22747565…	n-248.md Record
249	corrects Nagamochi 2005	open=	16	✓ same	15.87120984…Hosono 2026	15.80522786…	$\frac{31}{2} - \frac{\sqrt{937}}{2}$ ≈ 0.19477213…	n-249.md Record
250	corrects Nagamochi 2005	open=	16	✓ same	15.90722469…Hosono 2026	15.83786165…	$\frac{31}{2} - \frac{\sqrt{941}}{2}$ ≈ 0.16213834…	n-250.md Record
251	corrects Nagamochi 2005	open=	16	✓ same	15.94314647…Hosono 2026	15.87042614…	$\frac{31}{2} - \frac{3 \sqrt{105}}{2}$ ≈ 0.12957385…	n-251.md Record
252	corrects Nagamochi 2005	open (reported proved)=	16	✓ same	16Daniel 2026	15.90292180…	$\frac{31}{2} - \frac{\sqrt{949}}{2}$ ≈ 0.09707819…	n-252.md Record
253		provedO=	16	✓ same	16Daniel 2026	✓ same	0	n-253.md Record
254	corrects Nagamochi 2005	provedO=	16	✓ same	16Nagamochi 2005	✓ same	0	n-254.md Record
255	corrects Nagamochi 2005	provedO=	16	✓ same	16Nagamochi 2005	✓ same	0	n-255.md Record
256		provedO=R	16	✓ same	16	✓ same	0	n-256.md Record
257	corrects Nagamochi 2005	open=	$13 + \frac{5}{2} \sqrt{2}$ ≈ 16.53553390…Ellsworth 2025	16.53553390…	$\frac{574 \sqrt{2}}{257} + \frac{3343}{257}$ ≈ 16.16637581…Green 2000defect recorded	16.03222456…	0.50330933…	n-257.md Record
258	corrects Nagamochi 2005	open=	16.56344800…Chaoweeraprasit 2026	✓ same	$\frac{574 \sqrt{2}}{257} + \frac{3343}{257}$ ≈ 16.16637581…Green 2000defect recorded	16.06438241…	0.49906558…	n-258.md Record
259	corrects Nagamochi 2005	open=	16.59137814…Chaoweeraprasit 2026	✓ same	$\frac{574 \sqrt{2}}{257} + \frac{3343}{257}$ ≈ 16.16637581…Green 2000defect recorded	16.09647396…	0.49490418…	n-259.md Record
260	corrects Nagamochi 2005	open=	16.63398250…Daniel 2026	✓ same	$\frac{574 \sqrt{2}}{257} + \frac{3343}{257}$ ≈ 16.16637581…Green 2000defect recorded	16.12849960…	0.50548289…	n-260.md Record
261	corrects Nagamochi 2005	open=	16.67877987…Xu 2026	✓ same	16.19248053…Hosono 2026	16.16045976…	0.51832011…	n-261.md Record
262	corrects Nagamochi 2005	open=	$16 + \frac{1}{2} \sqrt{2}$ ≈ 16.70710678…	16.70710678…	16.23432307…Hosono 2026	16.19235482…	0.51475195…	n-262.md Record
263	corrects Nagamochi 2005	open=	16.73316600…Chaoweeraprasit 2026	✓ same	16.27141390…Hosono 2026	16.22418519…	0.50898081…	n-263.md Record
264	corrects Nagamochi 2005	open=	16.77473513…Ostashev 2026	✓ same	16.30840309…Hosono 2026	16.25595125…	0.51878387…	n-264.md Record
265	corrects Nagamochi 2005	open=	$9 + \frac{11}{2} \sqrt{2}$ ≈ 16.77817459…	16.77817459…	16.34529148…Hosono 2026	16.28765340…	0.49052118…	n-265.md Record
266	corrects Nagamochi 2005	open=	16.82302875…Daniel 2026	✓ same	16.38213121…Hosono 2026	16.31929201…	0.50373673…	n-266.md Record
267	corrects Nagamochi 2005	open=	16.83881526…Xu 2026	✓ same	16.40768678…Hosono 2026	16.35086748…	0.48794778…	n-267.md Record
268	corrects Nagamochi 2005	open=	16.87436171…Vladislav Lavrentev 2026	✓ same	16.42914131…Hosono 2026	16.38238017…	0.49198154…	n-268.md Record
269	corrects Nagamochi 2005	open=	16.90151358…Chaoweeraprasit 2026	✓ same	16.45962819…Hosono 2026	16.41383046…	0.48768311…	n-269.md Record
270	corrects Nagamochi 2005	open=	16.92816225…Daniel 2026	✓ same	16.48984078…Hosono 2026	16.44521871…	0.48294353…	n-270.md Record
271	corrects Nagamochi 2005	open=	16.94894773…Daniel 2026	✓ same	16.52918032…Hosono 2026	16.47654530…	0.47240242…	n-271.md Record
272	corrects Nagamochi 2005	open=	16.96558647…Chaoweeraprasit 2026	✓ same	16.56508552…Hosono 2026	16.50781059…	0.45777588…	n-272.md Record
273	corrects Nagamochi 2005	open=	16.98392596…Couzo 2026	✓ same	16.60000000…Hosono 2026	16.53901493…	0.44491103…	n-273.md Record
274	corrects Nagamochi 2005	open=	17	✓ same	16.62527702…Hosono 2026	16.57015867…	$\frac{33}{2} - \frac{\sqrt{1033}}{2}$ ≈ 0.42984132…	n-274.md Record
275	corrects Nagamochi 2005	open=	17	✓ same	16.65912601…Hosono 2026	16.60124218…	$\frac{33}{2} - \frac{\sqrt{1037}}{2}$ ≈ 0.39875781…	n-275.md Record
276	corrects Nagamochi 2005	open=	17	✓ same	16.69308599…Hosono 2026	16.63226580…	$\frac{33}{2} - \frac{\sqrt{1041}}{2}$ ≈ 0.36773419…	n-276.md Record
277	corrects Nagamochi 2005	open=	17	✓ same	16.72727497…Hosono 2026	16.66322987…	$\frac{33}{2} - \frac{\sqrt{1045}}{2}$ ≈ 0.33677012…	n-277.md Record
278	corrects Nagamochi 2005	open=	17	✓ same	16.76106249…Hosono 2026	16.69413474…	$\frac{33}{2} - \frac{\sqrt{1049}}{2}$ ≈ 0.30586525…	n-278.md Record
279	corrects Nagamochi 2005	open=	17	✓ same	16.79477313…Hosono 2026	16.72498073…	$\frac{33}{2} - \frac{9 \sqrt{13}}{2}$ ≈ 0.27501926…	n-279.md Record
280	corrects Nagamochi 2005	open=	17	✓ same	16.81248633…Hosono 2026	16.75576820…	$\frac{33}{2} - \frac{\sqrt{1057}}{2}$ ≈ 0.24423179…	n-280.md Record
281	corrects Nagamochi 2005	open=	17	✓ same	16.84621702…Hosono 2026	16.78649747…	$\frac{33}{2} - \frac{\sqrt{1061}}{2}$ ≈ 0.21350252…	n-281.md Record
282	corrects Nagamochi 2005	open=	17	✓ same	16.87987121…Hosono 2026	16.81716887…	$\frac{33}{2} - \frac{\sqrt{1065}}{2}$ ≈ 0.18283112…	n-282.md Record
283	corrects Nagamochi 2005	open=	17	✓ same	16.91344943…Hosono 2026	16.84778272…	$\frac{33}{2} - \frac{\sqrt{1069}}{2}$ ≈ 0.15221727…	n-283.md Record
284	corrects Nagamochi 2005	open=	17	✓ same	16.94695218…Hosono 2026	16.87833935…	$\frac{33}{2} - \frac{\sqrt{1073}}{2}$ ≈ 0.12166064…	n-284.md Record
285	corrects Nagamochi 2005	open (reported proved)=	17	✓ same	17Daniel 2026	16.90883908…	$\frac{33}{2} - \frac{\sqrt{1077}}{2}$ ≈ 0.09116091…	n-285.md Record
286		provedO=	17	✓ same	17Daniel 2026	✓ same	0	n-286.md Record
287	corrects Nagamochi 2005	provedO=	17	✓ same	17Nagamochi 2005	✓ same	0	n-287.md Record
288	corrects Nagamochi 2005	provedO=	17	✓ same	17Nagamochi 2005	✓ same	0	n-288.md Record
289		provedO=R	17	✓ same	17	✓ same	0	n-289.md Record
290	corrects Nagamochi 2005	open=	$14 + \frac{5}{2} \sqrt{2}$ ≈ 17.53553390…	17.53553390…	$\frac{8 \sqrt{34}}{145} + 2 \sqrt{2} + \frac{2031}{145}$ ≈ 17.15703136…Green 2000defect recorded	17.03027525…	0.50525865…	n-290.md Record
291	corrects Nagamochi 2005	open=	$14 + \frac{5}{2} \sqrt{2}$ ≈ 17.53553390…	17.53553390…	$\frac{8 \sqrt{34}}{145} + 2 \sqrt{2} + \frac{2031}{145}$ ≈ 17.15703136…Green 2000defect recorded	17.06049516…	0.47503874…	n-291.md Record
292	corrects Nagamochi 2005	open=	17.59137814…Chaoweeraprasit 2026	✓ same	$\frac{8 \sqrt{34}}{145} + 2 \sqrt{2} + \frac{2031}{145}$ ≈ 17.15703136…Green 2000defect recorded	17.09066002…	0.50071812…	n-292.md Record
293	corrects Nagamochi 2005	open=	17.63398250…Daniel 2026	✓ same	$\frac{8 \sqrt{34}}{145} + 2 \sqrt{2} + \frac{2031}{145}$ ≈ 17.15703136…Green 2000defect recorded	17.12077013…	0.51321236…	n-293.md Record
294	corrects Nagamochi 2005	open=	$12 + 4 \sqrt{2}$ ≈ 17.65685424…	17.65685424…	17.17873535…Hosono 2026	17.15082580…	0.50602844…	n-294.md Record
295	corrects Nagamochi 2005	open=	$\frac{22 + 22 \sqrt{2}}{3}$ ≈ 17.70423279…Xu 2026	✓ same	17.21811117…Hosono 2026	17.18082731…	0.52340547…	n-295.md Record
296	corrects Nagamochi 2005	open=	$17 + \frac{1}{2} \sqrt{2}$ ≈ 17.70710678…	17.70710678…	17.25268226…Hosono 2026	17.21077496…	0.49633181…	n-296.md Record
297	corrects Nagamochi 2005	open=	17.74041728…Couzo 2026	✓ same	17.28717102…Hosono 2026	17.24066904…	0.49974824…	n-297.md Record
298	corrects Nagamochi 2005	open=	$10 + \frac{11}{2} \sqrt{2}$ ≈ 17.77817459…	17.77817459…	17.32157801…Hosono 2026	17.27050983…	0.50766476…	n-298.md Record
299	corrects Nagamochi 2005	open=	17.80123854…Daniel 2026	✓ same	17.35590383…Hosono 2026	17.30029761…	0.50094093…	n-299.md Record
300	corrects Nagamochi 2005	open=	17.82412338…Ellsworth 2025	✓ same	17.39057669…Hosono 2026	17.33003267…	0.49409070…	n-300.md Record
301	corrects Nagamochi 2005	open≈	17.84666719…Couzo 2026	✓ same	17.41201967…Hosono 2026	17.3597153	0.48695189…	n-301.md Record
302	corrects Nagamochi 2005	open=	17.87001385…PingYou Ltd 2026	✓ same	17.43342608…Hosono 2026	17.38934575…	0.48066809…	n-302.md Record
303	corrects Nagamochi 2005	open=	17.90697823…Vladislav Lavrentev 2026	✓ same	17.46198618…Hosono 2026	17.41892431…	0.48805391…	n-303.md Record
304	corrects Nagamochi 2005	open=	17.92689890…Kirill Tymchishin 2026	✓ same	17.49038298…Hosono 2026	17.44845125…	0.47844764…	n-304.md Record
305	corrects Nagamochi 2005	open=	17.95046648…Chaoweeraprasit 2026	✓ same	17.52722278…Hosono 2026	17.47792684…	0.47253963…	n-305.md Record
306	corrects Nagamochi 2005	open=	17.96343371…Couzo 2026	✓ same	17.56072945…Hosono 2026	17.50735135…	0.45608236…	n-306.md Record
307	corrects Nagamochi 2005	open=	17.97925128…ntumlnoob 2026	✓ same	17.59416114…Hosono 2026	17.53672503…	0.44252624…	n-307.md Record
308	corrects Nagamochi 2005	open=	17.99714912…Daniel 2026	✓ same	17.61662010…Hosono 2026	17.56604816…	0.43110095…	n-308.md Record
309	corrects Nagamochi 2005	open=	18	✓ same	17.64888751…Hosono 2026	17.59532099…	$\frac{35}{2} - \frac{\sqrt{1169}}{2}$ ≈ 0.40467900…	n-309.md Record
310	corrects Nagamochi 2005	open=	18	✓ same	17.68087672…Hosono 2026	17.62454378…	$\frac{35}{2} - \frac{\sqrt{1173}}{2}$ ≈ 0.37545621…	n-310.md Record
311	corrects Nagamochi 2005	open=	18	✓ same	17.71286701…Hosono 2026	17.65371679…	$\frac{35}{2} - \frac{\sqrt{1177}}{2}$ ≈ 0.34628320…	n-311.md Record
312	corrects Nagamochi 2005	open=	18	✓ same	17.74454687…Hosono 2026	17.68284027…	$\frac{35}{2} - \frac{\sqrt{1181}}{2}$ ≈ 0.31715972…	n-312.md Record
313	corrects Nagamochi 2005	open=	18	✓ same	17.77616332…Hosono 2026	17.71191447…	$\frac{35}{2} - \frac{\sqrt{1185}}{2}$ ≈ 0.28808552…	n-313.md Record
314	corrects Nagamochi 2005	open=	18	✓ same	17.80000000…Hosono 2026	17.74093964…	$\frac{35}{2} - \frac{\sqrt{1189}}{2}$ ≈ 0.25906035…	n-314.md Record
315	corrects Nagamochi 2005	open=	18	✓ same	17.82434500…Hosono 2026	17.76991603…	$\frac{35}{2} - \frac{\sqrt{1193}}{2}$ ≈ 0.23008396…	n-315.md Record
316	corrects Nagamochi 2005	open=	18	✓ same	17.85592246…Hosono 2026	17.79884389…	$\frac{35}{2} - \frac{3 \sqrt{133}}{2}$ ≈ 0.20115610…	n-316.md Record
317	corrects Nagamochi 2005	open=	18	✓ same	17.88743714…Hosono 2026	17.82772345…	$\frac{35}{2} - \frac{\sqrt{1201}}{2}$ ≈ 0.17227654…	n-317.md Record
318	corrects Nagamochi 2005	open=	18	✓ same	17.91888940…Hosono 2026	17.85655495…	$\frac{35}{2} - \frac{\sqrt{1205}}{2}$ ≈ 0.14344504…	n-318.md Record
319	corrects Nagamochi 2005	open=	18	✓ same	17.95027962…Hosono 2026	17.88533865…	$\frac{35}{2} - \frac{\sqrt{1209}}{2}$ ≈ 0.11466134…	n-319.md Record
320	corrects Nagamochi 2005	open (reported proved)=	18	✓ same	18Daniel 2026	17.91407476…	$\frac{35}{2} - \frac{\sqrt{1213}}{2}$ ≈ 0.08592523…	n-320.md Record
321		provedO=	18	✓ same	18Daniel 2026	✓ same	0	n-321.md Record
322	corrects Nagamochi 2005	provedO=	18	✓ same	18Nagamochi 2005	✓ same	0	n-322.md Record
323	corrects Nagamochi 2005	provedO=	18	✓ same	18Nagamochi 2005	✓ same	0	n-323.md Record
324		provedO=R	18	✓ same	18	✓ same	0	n-324.md Record