import sympy
def isp_list(li):
    isln=[]
    for n in li:
        isln.append(sympy.isprime(n))
    return isln
def checksm(a,b):
    co=True
    for i in range(b):
        if a[i]==False:
            co=False
    return(co)
c=1
p=2
while c>0:
    d=0
    s=[0 for i in range(c)]
    p=2
    while p>0:
        n=1
        t=[]
        for i in s:
            t.append(i+d**n)
            n=n+1
        s=t
        il=isp_list(s)
        sp=checksm(il,c)
        if sp ==True:
            print(c,p,s,il)
            p=-1
            c=c+1
        else:
            np=sympy.nextprime(p)
            d=np-p
            p=np