Table of selected mathematical constants

Abbreviations used:

I - irrational number, A - algebraic number, T - transcendental number, ? - unknown

Gen - General, NuT - Number theory, ChT - Chaos theory, Com - Combinatorics, Inf - Information theory, Ana - Mathematical analysis

Symbol	Approximate Value	Name	Field	N	First Described	# of Known Digits
π	≈ 3.14159 26535 89793 23846 26433 83279 50288	Pi, Archimedes' constant or Ludolph's number	Gen, Ana	T	by c. 2000 BC	1,241,100,000,000
e	≈ 2.71828 18284 59045 23536 02874 71352 66249	Napier's constant, base of Natural logarithm	Gen, Ana	T	1618	50,100,000,000
√2	≈ 1.41421 35623 73095 04880 16887 24209 69807	Pythagoras' constant, square root of two	Gen	I A	by c. 800 BC	137,438,953,444
√3	≈ 1.73205 08075 68877 29352 74463 41505	Theodorus' constant, square root of three	Gen	I A	by c. 800 BC
γ	≈ 0.57721 56649 01532 86060 65120 90082 40243	Euler-Mascheroni constant	Gen, NuT		1735	108,000,000
φ	≈ 1.61803 39887 49894 84820 45868 34365 63811	Golden ratio	Gen	A	by 3rd century BC	3,141,000,000
β^*	≈ 0.70258	Embree-Trefethen constant	NuT
δ	≈ 4.66920 16091 02990 67185 32038 20466 20161	Feigenbaum constant	ChT		1975
α	≈ 2.50290 78750 95892 82228 39028 73218 21578	Feigenbaum constant	ChT
C2	≈ 0.66016 18158 46869 57392 78121 10014 55577	Twin prime constant	NuT			5,020
M1	≈ 0.26149 72128 47642 78375 54268 38608 69585	Meissel-Mertens constant	NuT		1866 1874	8,010
B2	≈ 1.90216 05823	Brun's constant for twin prime	NuT		1919	10
B4	≈ 0.87058 83800	Brun's constant for prime quadruplets	NuT
Λ	> – 2.7 · 10^-9	de Bruijn-Newman constant	NuT		1950?
K	≈ 0.91596 55941 77219 01505 46035 14932 38411	Catalan's constant	Com			201,000,000
K	≈ 0.76422 36535 89220 66	Landau-Ramanujan constant	NuT	I (?)		30,010
K	≈ 1.13198 824	Viswanath's constant	NuT			8
B´L	= 1	Legendre's constant	NuT
μ	≈ 1.45136 92348 83381 05028 39684 85892 027	Ramanujan-Soldner constant	NuT			75,500
EB	≈ 1.60669 51524 15291 763	Erdős–Borwein constant	NuT	I
Ω	depends on computation model	Chaitin's constant	Inf	T
β	≈ 0.28016 94990	Bernstein's constant	Ana
λ	≈ 0.30366 30029	Gauss-Kuzmin-Wirsing constant	Com		1974	385
D(1)	≈ 0.35323 63719	Hafner-Sarnak-McCurley constant	NuT		1993
λ, μ	≈ 0.62432 99885	Golomb-Dickman constant	Com NuT		1930 1964
	≈ 0.62946 50204	Cahen's constant
	≈ 0.66274 34193	Laplace limit
	≈ 0.80939 40205	Alladi-Grinstead constant	NuT
Λ	≈ 1.09868 58055	Lengyel's constant	Com		1992
	≈ 1.18656 91104	Khinchin-Lévy constant	NuT
	≈ 1.20205 69031 59594 28539 97381	Apéry's constant			1979	1,000,000,000
θ	≈ 1.30637 78838 63080 69046	Mills' constant	NuT	?	1947
	≈ 1.45607 49485 82689 67139 95953 51116 54356	Backhouse's constant
	≈ 1.46707 80794	Porter's constant	NuT		1975
	≈ 1.53960 07178	Lieb's square ice constant	Com		1967
	≈ 1.70521 11401 05367	Niven's constant	NuT		1969
	≈ 2.58498 17596	Sierpiński's constant
	≈ 2.68545 2001	Khinchin's constant	NuT	?	1934	7350
F	≈ 2.80777 02420	Fransén-Robinson constant	Ana
L	≈ .5	Landau's constant	Ana			1