Mathematical Constant - Table of Selected Mathematical Constants

Table of Selected Mathematical Constants

Abbreviations used:

R – Rational number, I – Irrational number (may be algebraic or transcendental), A – Algebraic number (irrational), T - Transcendental number (irrational)
Gen – General, NuT – Number theory, ChT – Chaos theory, Com – Combinatorics, Inf – Information theory, Ana – Mathematical analysis
Symbol Value Name Field N First Described # of Known Digits
0 = 0 Zero Gen R c. 7th–5th century BC N/A
1 = 1 One, Unity Gen R N/A
i = Imaginary unit, unit imaginary number Gen, Ana A 16th century N/A
≈ 3.14159 26535 89793 23846 26433 83279 50288 Pi, Archimedes' constant or Ludolph's number Gen, Ana T by c. 2000 BC 10,000,000,000,000
e ≈ 2.71828 18284 59045 23536 02874 71352 66249 e, Napier's constant, or Euler's number Gen, Ana T 1618 100,000,000,000
√2 ≈ 1.41421 35623 73095 04880 16887 24209 69807 Pythagoras' constant, square root of 2 Gen A by c. 800 BC 137,438,953,444
√3 ≈ 1.73205 08075 68877 29352 74463 41505 87236 Theodorus' constant, square root of 3 Gen A by c. 800 BC
√5 ≈ 2.23606 79774 99789 69640 91736 68731 27623 square root of 5 Gen A by c. 800 BC
≈ 0.57721 56649 01532 86060 65120 90082 40243 Euler–Mascheroni constant Gen, NuT 1735 14,922,244,771
≈ 1.61803 39887 49894 84820 45868 34365 63811 Golden ratio Gen A by 3rd century BC 100,000,000,000
≈ 1.32471 79572 44746 02596 09088 54478 09734 Plastic constant NuT A 1928
* ≈ 0.70258 Embree–Trefethen constant NuT
≈ 4.66920 16091 02990 67185 32038 20466 20161 Feigenbaum constant ChT 1975
≈ 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 primes NuT 1919 10
B4 ≈ 0.87058 83800 Brun's constant for prime quadruplets NuT
≥ –2.7 • 10−9 de Bruijn–Newman constant NuT 1950? none
K ≈ 0.91596 55941 77219 01505 46035 14932 38411 Catalan's constant Com 15,510,000,000
K ≈ 0.76422 36535 89220 66299 06987 31250 09232 Landau–Ramanujan constant NuT 30,010
K ≈ 1.13198 824 Viswanath's constant NuT 8
B´L = 1 Legendre's constant NuT R N/A
≈ 1.45136 92348 83381 05028 39684 85892 02744 Ramanujan–Soldner constant NuT 75,500
EB ≈ 1.60669 51524 15291 76378 33015 23190 92458 Erdős–Borwein constant NuT I
≈ 0.28016 94990 23869 13303 Bernstein's constant Ana
≈ 0.30366 30028 98732 65859 74481 21901 55623 Gauss–Kuzmin–Wirsing constant Com 1974 385
≈ 0.35323 63718 54995 98454 Hafner–Sarnak–McCurley constant NuT 1993
, ≈ 0.62432 99885 43550 87099 29363 83100 83724 Golomb–Dickman constant Com, NuT 1930
1964
≈ 0.64341 05463 Cahen's constant T 1891 4000
≈ 0.66274 34193 49181 58097 47420 97109 25290 Laplace limit
≈ 0.80939 40205 Alladi–Grinstead constant NuT
≈ 1.09868 58055 Lengyel's constant Com 1992
≈ 3.27582 29187 21811 15978 76818 82453 84386 Lévy's constant NuT
≈ 1.20205 69031 59594 28539 97381 61511 44999 Apéry's constant I 1979 15,510,000,000
≈ 1.30637 78838 63080 69046 86144 92602 60571 Mills' constant NuT 1947 6850
≈ 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 76428 85514 53434 50816 Niven's constant NuT 1969
K ≈ 2.58498 17595 79253 21706 58935 87383 17116 Sierpiński's constant
≈ 2.68545 20010 65306 44530 97148 35481 79569 Khinchin's constant NuT 1934 7350
F ≈ 2.80777 02420 28519 36522 15011 86557 77293 Fransén-Robinson constant Ana
L ≈ 0.5 Landau's constant Ana 1
P2 ≈ 2.29558 71493 92638 07403 42980 49189 49039 Universal parabolic constant Gen T
Ω ≈ 0.56714 32904 09783 87299 99686 62210 35555 Omega constant Ana T
MRB ≈ 0.187859 MRB constant NuT 3:13GMT 1/11/1999 314,159
≈ 3.35988 56662 43177 55317 20113 02918 .... Reciprocal Fibonacci constant

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