f[x_]:=Mod[a x + c,m]

Bad LCG Random generator

a=4; c=1; m=63; x0=1;
BadRandom=NestList[f,x0,300];
ListPlot[BadRandom]

ZX81 Generator

m=2^16+1; c=0; a=75; x0=1;
FactorInteger[m]
ZX81Random=NestList[f,x0,10000];
ListPlot[ZX81Random]

blocks=Partition[ZX81Random,2];
ListPlot[blocks]

RANDU

m=2^31 ;c=0; a=65539; x0=1;
RANDURandom=NestList[f,x0,50000];
ListPlot[RANDURandom]

blocks=Partition[RANDURandom,2];
ListPlot[blocks]

blocks3=Partition[RANDURandom,3];
ListPointPlot3D[blocks3]

Rotate the 3d picture in case you do not see the planes ...

Marsaglia

m=2^32 ;c=1; a=69069; x0=1;
MarsagliaRandom=NestList[f,x0,50000];
ListPlot[MarsagliaRandom]

blocks=Partition[MarsagliaRandom,2];
ListPlot[blocks]

blocks3=Partition[MarsagliaRandom,3];
ListPointPlot3D[blocks3]

Random Permutations

RandomPerm[n_]:=Module[{x=Range[n],k,a},
Do[
k=RandomInteger[{i,n}];
a=x[[i]]; x[[i]]=x[[k]]; x[[k]]=a;
,{i,1,n-1}]
Print[x]
]

RandomPerm[10]