a(n,k,b)=my(v=[]);for(r=1,length(digits(n,b)),if(r+length(digits(k,2))-length(digits(n,b))>0 && digits(k,2)[r+length(digits(k,2))-length(digits(n,b))]==1,v=concat(v,digits(n,b)[r])));fromdigits(v,b)

is(n,b)=for(k=1,2^length(digits(n,b))-2,if(ispseudoprime(a(n,k,b)) && a(n,k,b)>=b,return(0)));1

c(b)=my(v=[]);forprime(p=b+1,b^3,if(is(p,b),v=concat(v,p)));v

ML(x,z,b)=my(v=[]);for(y=0,b-1,if(is(x*b^2+y*b+z,b),v=concat(v,y)));v

L(b)=my(v=[]);for(x=1,b-1,for(z=1,b-1,if(gcd(z,b)==1,v=concat(v,[[x,ML(x,z,b),z]]))));v

issimple(k)=sum(r=1,length(k),setisset(k[r]))==1

s(k)=concat(x(k),u(k))

t(k)=my(v=[s(k)]);for(r=1,length(y(k)),v=concat(v,[concat(concat(x(k),concat(y(k)[r],[y(k)])),u(k))]));v

u(k)=my(v=[]);for(r=w(k)+1,length(k),v=concat(v,[k[r]]));v

w(k)=for(r=1,length(k),if(setisset(k[r]),return(r)))

ww(k)=my(v=[]);for(r=1,length(k),if(setisset(k[r]),v=concat(v,r)));v

x(k)=my(v=[]);for(r=1,w(k)-1,v=concat(v,k[r]));v

y(k)=k[w(k)]

z(k)=my(v=[]);for(r=w(k)+1,length(k),v=concat(v,k[r]));v

xx(b,k)=fromdigits(x(k),b)

yy(b,k)=y(k)[1]

zz(b,k)=fromdigits(z(k),b)

value(b,k,n)=xx(b,k)*b^(n+length(z(k)))+yy(b,k)*b^length(z(k))*(b^n-1)/(b-1)+zz(b,k)

aa(b,k)=xx(b,k)*b^length(z(k))*dd(b,k)+yy(b,k)*b^length(z(k))*dd(b,k)/(b-1)

bb(b,k)=b

cc(b,k)=zz(b,k)*dd(b,k)-yy(b,k)*b^length(z(k))*dd(b,k)/(b-1)

dd(b,k)=(b-1)/gcd(b-1,yy(b,k))

smpf(n)=forprime(p=2,50000,if(n%p==0,return(0)));1

numcov(b,k)=for(n=1,5000,if(smpf(value(b,k,n)),return(0)));1

nonsimplenumcov(b,k)=

algcov(b,k)=forprime(p=2, 16, if((ispower(aa(b,k),p) && ispower(bb(b,k),p) && ispower(-cc(b,k),p)) || (ispower(4*aa(b,k)*cc(b,k),4) && ispower(bb(b,k),4), return(1))); 0

combcov1(b,k)=forprime(p=5, 1201, if((issquare(aa(b,k)) && issquare(-cc(b,k)) && (aa(b,k)+cc(b,k))%p==0 && bb(b,k)%p==p-1) || (issquare(aa(b,k)*bb(b,k)) && issquare(-cc(b,k)) && (aa(b,k)*bb(b,k)+cc(b,k))%p==0 && bb(b,k)%p==p-1), return(1))); 0

combcov2(b,k)=for(r=3, 16, if((issquare(aa(b,k)) && issquare(-cc(b,k)) && (aa(b,k)+cc(b,k))%(2^r)==2^(r-1) && bb(b,k)%(2^r)==2^(r-1)+1) || (issquare(aa(b,k)*bb(b,k)) && issquare(-cc(b,k)) && (aa(b,k)*bb(b,k)+cc(b,k))%(2^r)==2^(r-1) && bb(b,k)%(2^r)==2^(r-1)+1), return(1))); 0

ac(b,k)=numcov(b,k) || algcov(b,k) || combcov1(b,k) || combcov2(b,k)

minimal(b)=my(M=c(b),L=L(b));