index of important irrational constants

The following table lists some of the most important irrational constants in mathematics.

Of course importance is sometimes debatable. Hardly anyone disputes the importance of π or e (in fact, these are the only two constants in the OEIS to have the keyword “core” attached to them), but for other constants it is not quite clear cut. In general, if a given constant has a name (especially a name hyphenating two famous mathematicians’ last names) I consider it important.

Irrationality is not always clear cut either, e.g., it might be a mistake to exclude the Euler-Mascheroni constant γ from this list.

The constants are given to 20 decimal places.

0.1149420448532962007 Kepler-Bouwkamp constant or polygon-inscribing constant
0.1234567891011121314 Champernowne’s constant C10
0.2078795763507619085 ii (has no imaginary part) or e-π2
0.2357111317192329313ős constant
0.2614972128476427837 Meissel-Mertens constant
0.3275822918721811159 Lévy’s constant
0.4146825098511116602 The prime constant ρ
0.5926327182016361971 Lehmer’s constant
0.6079271018540266286 6π2, the probability that a random integer is squarefreeMathworldPlanetmath
0.6434105462883380261 Cahen’s constant
0.7642236535892206629 Landau-Ramanujan constant
0.8346268416740731862 Gauss’s constant
0.8862269254527580136 Γ(32)=12π
0.9159655941772190150 Catalan’s constant K
1.2020569031595942853 Apéry’s constant ζ(3)
1.2254167024651776451 Γ(34)
1.3063778838630806904 Mills’ constant
1.3247179572447460260 The plastic constant
1.4142135623730950488 Square rootMathworldPlanetmath of two 2
1.4513692348833810502 Ramanujan-Soldner constant
1.6066951524152917637 Erdős-Borwein constant
1.6180339887498948482 The golden ratioMathworldPlanetmath ϕ
1.6449340668482264364 ζ(2)=π26, the solution to the Basel problemMathworldPlanetmath
1.7320508075688772935 Square root of three 3
1.7579327566180045327 Vijayaraghavan’s infinite nested radical 1+2+3+4+5+
1.7724538509055160273 Γ(12)=π
2.2360679774997896964 Square root of five 5
2.6651441426902251887 22
2.6854520010653064453 Khinchin’s constant
2.4142135623730950488 The silver ratio δS
2.5849817595792532170 Sierpiński’s constant
2.7182818284590452354 The natural log base e
3.1415926535897932385 The ratio of a circle’s radius to its circumferenceMathworldPlanetmath π
3.6256099082219083119 Γ(14)
4.1327313541224929385 2eπ
4.6692116609102990671 Feigenbaum’s constant δ
7.3890560989306502272 e2
14.1347251417346937904 The imaginary part of the first nontrivial zero of the Riemann zeta functionDlmfDlmfMathworldPlanetmath (the real part is 12)
15.1542622414792641898 ee
36.4621596072079117710 ππ

In looking these up in the OEIS, you can simply type them with a decimal point and no commas between the digits. If you get no results, try chopping off a couple of the least significant digits.


  • 1 Alan Jeffrey, Handbook of Mathematical Formulas and Integrals, 3rd Edition. New York: Elsevier Academic Press (2004): 223, Section 11.1.4 Special values of Γ(x)
Title index of important irrational constants
Canonical name IndexOfImportantIrrationalConstants
Date of creation 2013-03-22 17:03:10
Last modified on 2013-03-22 17:03:10
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 17
Author PrimeFan (13766)
Entry type Topic
Classification msc 00A08