Tests de primalité

n n = 561
n
a L n = 561
m= 9 746 347 772 161 m
n>1k>1
n n
1/2k
n
n
a
ba>1b>1
n>3
p n (p−1) |(n−1) F×
p
n n
1
n
663 867 935 1105 1547 1729 2077 2465 2647 2821 172081

p1= 6m+ 1 p2= 12m+ 1 p3= 18m+ 1
m m
p1p2p3
1
5
p p Mp= 2p−1
n2n−1
(sn)n>0
s0= 4 , si+1 =s2
i−2, i >0.
Mpsp−2≡0( mod Mp)
p
p
Mp
i si=ω2i+ω2i
ω= 2 + √3ω= 2 −√3sp−2≡0(mod Mp)
k ω2p−1=kMpω2p−2−1
Mpq Mp
ϕ:Z[√3] →Fq[t]/(t2−3) ϕ(ω)
2pFq[t]/(t2−3)
Mp3
Mp
2Mp
σ= 2√3FMp(√3) (6 + σ)Mp= 6 −σ
ω= (6 + σ)2/24 ωMp+1
2=−1
sp−2≡0 (mod Mp)ωMp+1
4
ω ω