g=25857960803
h=20101567521
p=34359738421
N=p-1

def Shanks(g,h,p,N):
    n=floor(sqrt(N).numerical_approx())+1
    L1=[]
    L1.append(1)

    for i in range(n+1):
        L1.append((L1[i-1]*g)%p)
    gn=L1[n].inverse_mod(p)
    l2=h
    j=0

    while j<n+1 :
        for i in range(n+1):
            if l2==L1[i]:
                x=i+n*j
                break
        l2=(l2*gn)%p
        j=j+1
    return x

t=cputime()
Shanks(g,h,p,N)
#g.powermod(1099511627791)
#print(randint(1,p-1))
#rozw=25303478531
cputime(t)

p=next_prime(2^35)
F=GF(p)
g=F.random_element()
N=g.multiplicative_order()

N % (p-1)
g
h
p