binom(2n,n).html

Faktorisierung von `binomial(2n,n)`

n p² ≤ 2n 2n < p²
p ≤ 2n/3 2n/3 < p ≤ n n < p ≤ 2n
10 (2)^2 (11)*(13)*(17)*(19)
11 (2)^3*(3) (7) (13)*(17)*(19)
12 (2)^2 (7) (13)*(17)*(19)*(23)
13 (2)^3*(5)^2 (7) (17)*(19)*(23)
14 (2)^3*(3)^3*(5)^2 (17)*(19)*(23)
15 (2)^4*(3)^2*(5) (17)*(19)*(23)*(29)
16 (2)*(3)^2*(5) (17)*(19)*(23)*(29)*(31)
17 (2)^2*(3)^3*(5) (11) (19)*(23)*(29)*(31)
18 (2)^2*(3)*(5)^2 (7)*(11) (19)*(23)*(29)*(31)
19 (2)^3*(3)*(5)^2 (7)*(11) (23)*(29)*(31)*(37)
20 (2)^2*(3)^2*(5) (7)*(11)*(13) (23)*(29)*(31)*(37)
21 (2)^3*(3)*(5) (11)*(13) (23)*(29)*(31)*(37)*(41)
22 (2)^3*(3)*(5) (13) (23)*(29)*(31)*(37)*(41)*(43)
23 (2)^4*(3)^3*(5)^2 (13) (29)*(31)*(37)*(41)*(43)
24 (2)^2*(3)^2*(5)^2 (13) (29)*(31)*(37)*(41)*(43)*(47)
25 (2)^3*(3)^2*(7)^2 (13) (29)*(31)*(37)*(41)*(43)*(47)
26 (2)^3*(3)^3*(7)^2 (17) (29)*(31)*(37)*(41)*(43)*(47)
27 (2)^4*(7)^2 (17) (29)*(31)*(37)*(41)*(43)*(47)*(53)
28 (2)^3*(5)*(7) (11)*(17) (29)*(31)*(37)*(41)*(43)*(47)*(53)
29 (2)^4*(3)*(5)*(7) (11)*(17)*(19) (31)*(37)*(41)*(43)*(47)*(53)
30 (2)^4*(7) (11)*(17)*(19) (31)*(37)*(41)*(43)*(47)*(53)*(59)
31 (2)^5*(7) (11)*(17)*(19) (37)*(41)*(43)*(47)*(53)*(59)*(61)
32 (2)*(3)^2*(7)^2 (11)*(17)*(19) (37)*(41)*(43)*(47)*(53)*(59)*(61)
33 (2)^2*(3)*(5)*(7)^2 (13)*(17)*(19) (37)*(41)*(43)*(47)*(53)*(59)*(61)
34 (2)^2*(3)*(5)*(7)^2 (13)*(19) (37)*(41)*(43)*(47)*(53)*(59)*(61)*(67)
35 (2)^3*(3)^2*(7) (13)*(19)*(23) (37)*(41)*(43)*(47)*(53)*(59)*(61)*(67)
36 (2)^2*(7) (13)*(19)*(23) (37)*(41)*(43)*(47)*(53)*(59)*(61)*(67)*(71)
37 (2)^3*(7) (13)*(19)*(23) (41)*(43)*(47)*(53)*(59)*(61)*(67)*(71)*(73)
38 (2)^3*(3)*(5)^2*(7) (13)*(23) (41)*(43)*(47)*(53)*(59)*(61)*(67)*(71)*(73)
39 (2)^4*(5)^2*(7)^2 (11)*(23) (41)*(43)*(47)*(53)*(59)*(61)*(67)*(71)*(73)
40 (2)^2*(5)*(7)^2 (11)*(23) (41)*(43)*(47)*(53)*(59)*(61)*(67)*(71)*(73)*(79)

n	p² ≤ 2n	2n < p² p ≤ 2n/3	n < p ≤ 2n
10	(2)^2		(11)(13)(17)*(19)
11	(2)^3*(3)	(7)	(13)(17)(19)
12	(2)^2	(7)	(13)(17)(19)*(23)
13	(2)^3*(5)^2	(7)	(17)(19)(23)
14	(2)^3(3)^3(5)^2		(17)(19)(23)
15	(2)^4(3)^2(5)		(17)(19)(23)*(29)
16	(2)(3)^2(5)		(17)(19)(23)(29)(31)
17	(2)^2(3)^3(5)	(11)	(19)(23)(29)*(31)
18	(2)^2(3)(5)^2	(7)*(11)	(19)(23)(29)*(31)
19	(2)^3(3)(5)^2	(7)*(11)	(23)(29)(31)*(37)
20	(2)^2(3)^2(5)	(7)(11)(13)	(23)(29)(31)*(37)
21	(2)^3(3)(5)	(11)*(13)	(23)(29)(31)(37)(41)
22	(2)^3(3)(5)	(13)	(23)(29)(31)(37)(41)*(43)
23	(2)^4(3)^3(5)^2	(13)	(29)(31)(37)(41)(43)
24	(2)^2(3)^2(5)^2	(13)	(29)(31)(37)(41)(43)*(47)
25	(2)^3(3)^2(7)^2	(13)	(29)(31)(37)(41)(43)*(47)
26	(2)^3(3)^3(7)^2	(17)	(29)(31)(37)(41)(43)*(47)
27	(2)^4*(7)^2	(17)	(29)(31)(37)(41)(43)(47)(53)
28	(2)^3(5)(7)	(11)*(17)	(29)(31)(37)(41)(43)(47)(53)
29	(2)^4(3)(5)*(7)	(11)(17)(19)	(31)(37)(41)(43)(47)*(53)
30	(2)^4*(7)	(11)(17)(19)	(31)(37)(41)(43)(47)(53)(59)
31	(2)^5*(7)	(11)(17)(19)	(37)(41)(43)(47)(53)(59)(61)
32	(2)(3)^2(7)^2	(11)(17)(19)	(37)(41)(43)(47)(53)(59)(61)
33	(2)^2(3)(5)*(7)^2	(13)(17)(19)	(37)(41)(43)(47)(53)(59)(61)
34	(2)^2(3)(5)*(7)^2	(13)*(19)	(37)(41)(43)(47)(53)(59)(61)*(67)
35	(2)^3(3)^2(7)	(13)(19)(23)	(37)(41)(43)(47)(53)(59)(61)*(67)
36	(2)^2*(7)	(13)(19)(23)	(37)(41)(43)(47)(53)(59)(61)(67)(71)
37	(2)^3*(7)	(13)(19)(23)	(41)(43)(47)(53)(59)(61)(67)(71)(73)
38	(2)^3(3)(5)^2*(7)	(13)*(23)	(41)(43)(47)(53)(59)(61)(67)(71)(73)
39	(2)^4(5)^2(7)^2	(11)*(23)	(41)(43)(47)(53)(59)(61)(67)(71)(73)
40	(2)^2(5)(7)^2	(11)*(23)	(41)(43)(47)(53)(59)(61)(67)(71)(73)*(79)

Zum Vergleich: Die Primzahlen p ≤ 80

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79

Noch ein Beispiel: n = 100

n p² ≤ 2n 2n < p²
p ≤ 2n/3 2n/3 < p ≤ n n < p ≤ 2n
100 (2)^3*(3)*(5)*(11)*(13)^2 (17)*(37)*(53)*(59)*(61) (101)*(103)*(107)*(109)*(113)*(127)*(131) *(137)*(139)*(149)*(151)*(157)*(163)*(167) *(173)*(179)*(181)*(191)*(193)*(197)*(199)

Faktorisierung von binomial(2n,n)

Zum Vergleich: Die Primzahlen p ≤ 80

Noch ein Beispiel: n = 100

Faktorisierung von `binomial(2n,n)`