Fundamental article: List of numerical constants
Truncations utilized:
R – Rational number, I – Irrational number (may be logarithmic or transcendental), A – Algebraic number (unreasonable), T – Transcendental number (silly)
Gen – General, Nut – Number hypothesis, Cht – Chaos hypothesis, Com – Combinatorics, Inf – Information hypothesis, Ana – Mathematical investigation
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
= √–1 imaginary unit, unit nonexistent number gen, Ana a 16th century n/A
π
≈ 3.14159 26535 89793 23846 26433 83279 50288 pi, Archimedes' steady or Ludolph's number gen, Ana t by c. 2000 Bc 10,000,000,000,000[27]
e
≈ 2.71828 18284 59045 23536 02874 71352 66249 e, Napier's steady, or Euler's number gen, Ana t 1618 100,000,000,000
√2
≈ 1.41421 35623 73095 04880 16887 24209 69807 pythagoras' steady, square base of 2 gen a by c. 800 Bc 137,438,953,444
√3
≈ 1.73205 08075 68877 29352 74463 41505 87236 theodorus' steady, square base of 3 gen a by c. 800 BC
√5
≈ 2.23606 79774 99789 69640 91736 68731 27623 square foundation of 5 gen a by c. 800 BC
\gamma
≈ 0.57721 56649 01532 86060 65120 90082 40243 euler–mascheroni constant gen, Nut 1735 14,922,244,771
\phi
≈ 1.61803 39887 49894 84820 45868 34365 63811 golden ratio gen a by third century Bc 100,000,000,000
\rho
≈ 1.32471 79572 44746 02596 09088 54478 09734 plastic constant nut a 1928
\beta*
≈ 0.70258 embree–trefethen constant nut
\delta
≈ 4.66920 16091 02990 67185 32038 20466 20161 feigenbaum constant cht 1975
\alpha
≈ 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 consistent for twin primes nut 1919 10
B4
≈ 0.87058 83800 brun's consistent for prime quadruplets nut
\lambda
≥ –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
\mu
≈ 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
\beta
≈ 0.28016 94990 23869 13303 bernstein's constant[28] ana
\lambda
≈ 0.30366 30028 98732 65859 74481 21901 55623 gauss–kuzmin–wirsing constant com 1974 385
\sigma
≈ 0.35323 63718 54995 98454 hafner–sarnak–mccurley constant nut 1993
\lambda, \mu
≈ 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 utmost
≈ 0.80939 40205 alladi–grinstead constant[29] nut
\lambda
≈ 1.09868 58055 lengyel's constant[30] com 1992
≈ 3.27582 29187 21811 15978 76818 82453 84386 lévy's constant nut
\zeta (3)
≈ 1.20205 69031 59594 28539 97381 61511 44999 apéry's constant i 1979 15,510,000,000
\theta
≈ 1.30637 78838 63080 69046 86144 92602 60571 mills' constant nut 1947 6850
≈ 1.45607 49485 82689 67139 95953 51116 54356 backhouse's constant[31]
≈ 1.46707 80794 porter's constant[32] nut 1975
≈ 1.53960 07178 lieb's square ice constant[33] 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 consistent
≈ 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 illustrative constant gen t
Ω
≈ 0.56714 32904 09783 87299 99686 62210 35555 omega constant ana t
C_{{}_{mrb}}
Fundamental article: List of numerical constants
Truncations utilized:
R – Rational number, I – Irrational number (may be logarithmic or transcendental), A – Algebraic number (unreasonable), T – Transcendental number (silly)
Gen – General, Nut – Number hypothesis, Cht – Chaos hypothesis, Com – Combinatorics, Inf – Information hypothesis, Ana – Mathematical investigation
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
= √–1 imaginary unit, unit nonexistent number gen, Ana a 16th century n/A
π
≈ 3.14159 26535 89793 23846 26433 83279 50288 pi, Archimedes' steady or Ludolph's number gen, Ana t by c. 2000 Bc 10,000,000,000,000[27]
e
≈ 2.71828 18284 59045 23536 02874 71352 66249 e, Napier's steady, or Euler's number gen, Ana t 1618 100,000,000,000
√2
≈ 1.41421 35623 73095 04880 16887 24209 69807 pythagoras' steady, square base of 2 gen a by c. 800 Bc 137,438,953,444
√3
≈ 1.73205 08075 68877 29352 74463 41505 87236 theodorus' steady, square base of 3 gen a by c. 800 BC
√5
≈ 2.23606 79774 99789 69640 91736 68731 27623 square foundation of 5 gen a by c. 800 BC
\gamma
≈ 0.57721 56649 01532 86060 65120 90082 40243 euler–mascheroni constant gen, Nut 1735 14,922,244,771
\phi
≈ 1.61803 39887 49894 84820 45868 34365 63811 golden ratio gen a by third century Bc 100,000,000,000
\rho
≈ 1.32471 79572 44746 02596 09088 54478 09734 plastic constant nut a 1928
\beta*
≈ 0.70258 embree–trefethen constant nut
\delta
≈ 4.66920 16091 02990 67185 32038 20466 20161 feigenbaum constant cht 1975
\alpha
≈ 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 consistent for twin primes nut 1919 10
B4
≈ 0.87058 83800 brun's consistent for prime quadruplets nut
\lambda
≥ –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
\mu
≈ 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
\beta
≈ 0.28016 94990 23869 13303 bernstein's constant[28] ana
\lambda
≈ 0.30366 30028 98732 65859 74481 21901 55623 gauss–kuzmin–wirsing constant com 1974 385
\sigma
≈ 0.35323 63718 54995 98454 hafner–sarnak–mccurley constant nut 1993
\lambda, \mu
≈ 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 utmost
≈ 0.80939 40205 alladi–grinstead constant[29] nut
\lambda
≈ 1.09868 58055 lengyel's constant[30] com 1992
≈ 3.27582 29187 21811 15978 76818 82453 84386 lévy's constant nut
\zeta (3)
≈ 1.20205 69031 59594 28539 97381 61511 44999 apéry's constant i 1979 15,510,000,000
\theta
≈ 1.30637 78838 63080 69046 86144 92602 60571 mills' constant nut 1947 6850
≈ 1.45607 49485 82689 67139 95953 51116 54356 backhouse's constant[31]
≈ 1.46707 80794 porter's constant[32] nut 1975
≈ 1.53960 07178 lieb's square ice constant[33] 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 consistent
≈ 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 illustrative constant gen t
Ω
≈ 0.56714 32904 09783 87299 99686 62210 35555 omega constant ana t
C_{{}_{mrb}}
Truncations utilized:
R – Rational number, I – Irrational number (may be logarithmic or transcendental), A – Algebraic number (unreasonable), T – Transcendental number (silly)
Gen – General, Nut – Number hypothesis, Cht – Chaos hypothesis, Com – Combinatorics, Inf – Information hypothesis, Ana – Mathematical investigation
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
= √–1 imaginary unit, unit nonexistent number gen, Ana a 16th century n/A
π
≈ 3.14159 26535 89793 23846 26433 83279 50288 pi, Archimedes' steady or Ludolph's number gen, Ana t by c. 2000 Bc 10,000,000,000,000[27]
e
≈ 2.71828 18284 59045 23536 02874 71352 66249 e, Napier's steady, or Euler's number gen, Ana t 1618 100,000,000,000
√2
≈ 1.41421 35623 73095 04880 16887 24209 69807 pythagoras' steady, square base of 2 gen a by c. 800 Bc 137,438,953,444
√3
≈ 1.73205 08075 68877 29352 74463 41505 87236 theodorus' steady, square base of 3 gen a by c. 800 BC
√5
≈ 2.23606 79774 99789 69640 91736 68731 27623 square foundation of 5 gen a by c. 800 BC
\gamma
≈ 0.57721 56649 01532 86060 65120 90082 40243 euler–mascheroni constant gen, Nut 1735 14,922,244,771
\phi
≈ 1.61803 39887 49894 84820 45868 34365 63811 golden ratio gen a by third century Bc 100,000,000,000
\rho
≈ 1.32471 79572 44746 02596 09088 54478 09734 plastic constant nut a 1928
\beta*
≈ 0.70258 embree–trefethen constant nut
\delta
≈ 4.66920 16091 02990 67185 32038 20466 20161 feigenbaum constant cht 1975
\alpha
≈ 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 consistent for twin primes nut 1919 10
B4
≈ 0.87058 83800 brun's consistent for prime quadruplets nut
\lambda
≥ –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
\mu
≈ 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
\beta
≈ 0.28016 94990 23869 13303 bernstein's constant[28] ana
\lambda
≈ 0.30366 30028 98732 65859 74481 21901 55623 gauss–kuzmin–wirsing constant com 1974 385
\sigma
≈ 0.35323 63718 54995 98454 hafner–sarnak–mccurley constant nut 1993
\lambda, \mu
≈ 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 utmost
≈ 0.80939 40205 alladi–grinstead constant[29] nut
\lambda
≈ 1.09868 58055 lengyel's constant[30] com 1992
≈ 3.27582 29187 21811 15978 76818 82453 84386 lévy's constant nut
\zeta (3)
≈ 1.20205 69031 59594 28539 97381 61511 44999 apéry's constant i 1979 15,510,000,000
\theta
≈ 1.30637 78838 63080 69046 86144 92602 60571 mills' constant nut 1947 6850
≈ 1.45607 49485 82689 67139 95953 51116 54356 backhouse's constant[31]
≈ 1.46707 80794 porter's constant[32] nut 1975
≈ 1.53960 07178 lieb's square ice constant[33] 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 consistent
≈ 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 illustrative constant gen t
Ω
≈ 0.56714 32904 09783 87299 99686 62210 35555 omega constant ana t
C_{{}_{mrb}}
Fundamental article: List of numerical constants
Truncations utilized:
R – Rational number, I – Irrational number (may be logarithmic or transcendental), A – Algebraic number (unreasonable), T – Transcendental number (silly)
Gen – General, Nut – Number hypothesis, Cht – Chaos hypothesis, Com – Combinatorics, Inf – Information hypothesis, Ana – Mathematical investigation
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
= √–1 imaginary unit, unit nonexistent number gen, Ana a 16th century n/A
π
≈ 3.14159 26535 89793 23846 26433 83279 50288 pi, Archimedes' steady or Ludolph's number gen, Ana t by c. 2000 Bc 10,000,000,000,000[27]
e
≈ 2.71828 18284 59045 23536 02874 71352 66249 e, Napier's steady, or Euler's number gen, Ana t 1618 100,000,000,000
√2
≈ 1.41421 35623 73095 04880 16887 24209 69807 pythagoras' steady, square base of 2 gen a by c. 800 Bc 137,438,953,444
√3
≈ 1.73205 08075 68877 29352 74463 41505 87236 theodorus' steady, square base of 3 gen a by c. 800 BC
√5
≈ 2.23606 79774 99789 69640 91736 68731 27623 square foundation of 5 gen a by c. 800 BC
\gamma
≈ 0.57721 56649 01532 86060 65120 90082 40243 euler–mascheroni constant gen, Nut 1735 14,922,244,771
\phi
≈ 1.61803 39887 49894 84820 45868 34365 63811 golden ratio gen a by third century Bc 100,000,000,000
\rho
≈ 1.32471 79572 44746 02596 09088 54478 09734 plastic constant nut a 1928
\beta*
≈ 0.70258 embree–trefethen constant nut
\delta
≈ 4.66920 16091 02990 67185 32038 20466 20161 feigenbaum constant cht 1975
\alpha
≈ 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 consistent for twin primes nut 1919 10
B4
≈ 0.87058 83800 brun's consistent for prime quadruplets nut
\lambda
≥ –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
\mu
≈ 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
\beta
≈ 0.28016 94990 23869 13303 bernstein's constant[28] ana
\lambda
≈ 0.30366 30028 98732 65859 74481 21901 55623 gauss–kuzmin–wirsing constant com 1974 385
\sigma
≈ 0.35323 63718 54995 98454 hafner–sarnak–mccurley constant nut 1993
\lambda, \mu
≈ 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 utmost
≈ 0.80939 40205 alladi–grinstead constant[29] nut
\lambda
≈ 1.09868 58055 lengyel's constant[30] com 1992
≈ 3.27582 29187 21811 15978 76818 82453 84386 lévy's constant nut
\zeta (3)
≈ 1.20205 69031 59594 28539 97381 61511 44999 apéry's constant i 1979 15,510,000,000
\theta
≈ 1.30637 78838 63080 69046 86144 92602 60571 mills' constant nut 1947 6850
≈ 1.45607 49485 82689 67139 95953 51116 54356 backhouse's constant[31]
≈ 1.46707 80794 porter's constant[32] nut 1975
≈ 1.53960 07178 lieb's square ice constant[33] 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 consistent
≈ 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 illustrative constant gen t
Ω
≈ 0.56714 32904 09783 87299 99686 62210 35555 omega constant ana t
C_{{}_{mrb}}
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