| 1a |
Sidon set autocorrelation constant |
1.2802 |
1.5029 |
| 1b |
Erdős minimum overlap constant |
0.379005 |
0.380876 |
| 2 |
Crouzeix constant |
2 |
$1+\sqrt{2} \approx 2.4142$ |
| 3a |
Gyamarti-Hennecart-Ruzsa sum-difference constant |
1.173077 |
1.33333 |
| 3b |
Kakeya sums-differences constant |
>1.77898 |
1.83333 |
| 3c |
4-slope Kakeya-type sum-difference constant |
1.67471 |
1.75 |
| 4a |
Cap set constant |
2.2202 |
2.756 |
| 4b |
Furstenberg–Sárközy square-difference constant |
0.733412 |
1 |
| 5a |
Sidon set size constant |
0 |
0.97633 |
| 5b |
Sidon set density inside (4,5) sets |
0.5294 |
0.5714 |
| 6 |
Union-closed sets conjecture constant |
0.38271 |
0.5 |
| 7a |
Irrationality measure of $\pi$
|
2 |
7.103205334137 |
| 7b |
Irrationality measure of $\Gamma(1/4)$
|
2 |
$10^{143}$ |
| 8 |
Classical zero-free region constant |
0.755106 |
5.558691 |
| 9 |
Shannon capacity of the 7-cycle |
3.2578 |
3.3177 |
| 10a |
The real Grothendieck constant |
1.67696 |
1.782214 |
| 10b |
The complex Grothendieck constant |
1.338 |
1.40491 |
| 10c |
Spencer discrepancy constant (“six standard deviations suffice”) |
1.414214 |
3.674235 (3.65 unpublished) |
| 11a |
$L^1$ Poincaré constant on the Hamming cube |
$\sqrt{\pi/2} \approx 1.2533$ |
$\pi/2 - 0.00013 \approx 1.5707$ |
| 11b |
Critical exponent for isoperimetric inequality on the Hamming cube |
0.5 |
0.5 |
| 12 |
The Beardwood–Halton–Hammersley constant |
0.6277 |
0.90304 |
| 13a |
Moser's convex worm cover constant |
0.232239 |
0.2617993878 |
| 13b |
Lebesgue's convex universal cover constant |
0.832 |
0.8440935944 |
| 14 |
Smallest $n$ for which the value of $BB(n)$ is undecidable |
6 |
432 |
| 15a |
Matrix multiplication exponent |
2 |
2.371339 |
| 15b |
Dual matrix multiplication exponent |
>0.321334 |
1 |
| 16 |
Brezis–Gallouet–Wainger remainder constant on the 2D torus |
$\frac{\beta + \pi}{\pi} \approx 1.82283$ |
$\approx 2.15627$ |
| 17 |
Exponential growth constant of diagonal Ramsey numbers |
$\sqrt{2} \approx 1.4142$ |
3.7992027396 |
| 18 |
Marton's conjecture constant (PFR) |
1 |
9 |
| 19 |
Berry–Esseen constant |
0.4097321837 |
0.4690 |
| 20a |
Thin shell conjecture constant |
2 |
$< \infty$ |
| 20b |
Isotropic constant of a log-concave probability measure |
$1/e$ |
$< \infty$ |
| 20c |
KLS constant for log-concave probability measures |
$\sqrt{\pi/2} \approx 1.25331$ |
$\infty$ |
| 21 |
de Bruijn–Newman constant |
0 |
0.2 |
| 22a |
Tight knot constant |
1.105 |
10.76 |
| 22b |
Tight alternating knot constant |
0.017 |
7.31 |
| 23a |
Smallest unsolved instance of the Hadamard conjecture |
668 |
$\infty$ |
| 23b |
Minimal condition number decay for sign matrices |
$17/92$ |
1 |
| 24 |
Komlós discrepancy constant |
$1+\sqrt{2}$ |
$\infty$ |
| 25 |
Mahler volume product constant |
$\pi$ |
4 |
| 26a |
Bohnenblust--Hille constant on the Boolean cube |
$2$ |
$\infty$ |
| 26b |
Multilinear Bohnenblust--Hille constant (real) |
$2$ |
$\infty$ |
| 27a |
Chromatic number of the plane |
5 |
7 |
| 27b |
Maximum Chromatic Number of Biplanar Graphs |
9 |
12 |
| 28 |
Smallest dimension in which Borsuk’s conjecture fails |
4 |
64 |
| 29 |
Kissing number in dimension $5$
|
40 |
44 |
| 30 |
Stanley–Wilf limit for the permutation pattern $1324$
|
10.27 |
13.5 |
| 31 |
Chvátal–Sankoff constant for a binary alphabet |
0.792665992 |
0.826280 |
| 32 |
Constant term of one-shot channel simulation |
$-\log_2 \log_2 e \approx -0.53$ |
$\sum_{k=1}^{\infty}2^{-k-1}k\log_{2}k-\log_{2}\log_{2}e \approx 0.76$ |
| 33 |
Ihara constant over $\mathbb{F}_2$
|
0.316999... |
$\sqrt{2}-1 \approx 0.41421$ |
| 34 |
Falconer distance problem in $\mathbb{R}^2$
|
1 |
$5/4$ |
| 35 |
Gradient Descent Exponent |
$\log_2(1+\sqrt{2}) \approx 1.271$ |
2 |
| 36 |
Sphere packing density in $\mathbb{R}^4$
|
$\pi^2/16 \approx 0.616850$ |
0.644421 |
| 37 |
The degree--sensitivity exponent |
$\log_{3}(6) \approx 1.63093$ |
2 |
| 38 |
Square-lattice self-avoiding walk connective constant |
2.625622 |
2.679193 |
| 39 |
Hadwiger covering / illumination number in $\mathbb{R}^3$
|
8 |
14 |
| 40a |
Lehmer’s Mahler measure constant |
1 |
1.176280... |
| 40b |
Asymptotic Dobrowolski constant for Lehmer’s problem |
$9/4$ |
$\infty$ |
| 41 |
Moving sofa constant |
2.2195 |
2.37 (2.2195 announced) |
| 42 |
Turan's pure power sum constant |
0.5 |
0.69368 |
| 43 |
Gilbert-Pollak conjecture (Steiner ratio) |
0.8559 |
0.86602540378 |
| 44 |
Maximal number of relevant variables in degree-$d$ Boolean functions |
1.5 |
4.394 |
| 45 |
Density of odd integers that are the sum of a prime and a power of two |
0.107648 |
0.490341088858244 |
| 46 |
Fourier restriction constant for the 2-sphere |
3 |
$\frac{22}{7}\approx 3.142857$ |
| 47 |
Centered Hardy-Littlewood maximal constant in dimension $2$
|
$\frac{11+\sqrt{61}}{12}\approx 1.5675208$ |
9 |
| 48 |
Convex sub-Gaussian comparison constant |
1 |
$<\infty$ |
| 49 |
Erdős–Szemerédi $3$-sunflower-free capacity |
>1.551 (>=1.554 unpublished) |
$\frac{3}{2^{2/3}} \approx 1.88988$ |
| 50 |
Approximation ratio for quantum Max Cut |
0.611 |
$<1$ (0.5 for product states) |
| 51 |
Erdős maximum term problem |
0.5850788 |
$\frac{2}{\pi}\approx 0.63662$ |
| 52 |
Satisfiability threshold for random 3-SAT |
3.52 |
4.490 |
| 53 |
Davenport constant for $C_n^3$
|
3 |
20369 |
| 54 |
Beurling–Ahlfors transform constant |
1 |
1.575 |
| 55 |
Coefficient of the acyclic chromatic index |
1 |
3.142 |
| 56 |
$\mathrm{GL}_2$ Ramanujan conjecture exponent |
0 |
$\tfrac{7}{64}=0.109375$ |
| 57a |
Bloch’s constant |
$\frac{\sqrt{3}}{4}+2\times 10^{-4}$ |
$\dfrac{1}{\sqrt{1+\sqrt{3}}},\dfrac{\Gamma(1/3)\Gamma(11/12)}{\Gamma(1/4)}\approx 0.4719$ |
| 57b |
Landau's constant |
$\frac{1}{2}+10^{-335}$ |
$\dfrac{\Gamma(1/3)\Gamma(5/6)}{\Gamma(1/6)}\approx 0.5433$ |
| 57c |
Univalent Bloch constant |
0.5708858 |
1 |
| 58 |
Zaremba’s conjecture constant |
5 |
$\infty$ |
| 59 |
Bohr radius for the bidisc |
0.3006 |
0.3177 |
| 60 |
Favard-length decay exponent |
$\frac{1}{6}$ |
1 |
| 61 |
Selberg congruence spectral-gap constant |
0 |
$\frac{7}{64}$ |
| 62a |
Lindelof (pointwise growth) exponent for the Riemann zeta function |
0 |
$\frac{13}{84}$ |
| 62b |
Burgess-quality subconvexity exponent for Dirichlet $L$-functions |
0 |
$\frac{3}{16}$ |
| 63 |
Dirichlet divisor problem exponent |
$1/4$ |
$\frac{131}{416}$ |
| 64 |
Gauss circle problem exponent |
0 |
$\frac{131}{208}$ |
| 65 |
Linnik's constant |
1 |
5 |
| 66 |
Elliott-Halberstam level-of-distribution exponent |
$1/2$ |
1 |
| 67 |
Brennan's conjecture exponent |
3.422 |
4 |
| 68 |
Korenblum's constant |
0.28185 |
0.6778994 |
| 69 |
Sendov radius constant |
1 |
2 |
| 70 |
Reverse Brunn-Minkowski constant |
1 |
$<\infty$ |
| 71 |
Fourier Entropy-Influence constant |
6.278 |
$\infty$ |
| 72 |
Polya-Vinogradov best constant (squarefree asymptotic) |
0 |
$\frac{1}{4\pi}\approx 0.07958$ |
| 73 |
Flatness constant in dimension 3 |
$2+\sqrt{2}$ |
$<3.972$ |
| 74 |
10-point multi-point Seshadri constant on $\mathbb{P}^2$
|
$\frac{117}{370}$ |
$\frac{1}{\sqrt{10}}$ |
| 75 |
Metric TSP subtour-LP integrality-gap constant |
$\frac{4}{3}$ |
$\frac{3}{2} - 2.18 \cdot 10^{-34}$ |