#!/usr/bin/env python3
import json,urllib.request as u
a=10000;b=10001
r=json.load(u.urlopen(u.Request('https://factordb.com/rpc',json.dumps(dict(jsonrpc='2.0',id=1,method='get_family',params=dict(expr='10^18+n',start=a,limit=b-a,factors=True))).encode(),{'Content-Type':'application/json'}),timeout=6))['result']['members']
def bad(q):return q%3==1 and pow(2,(q-1)//3,q)!=1
g=[m['x'] for m in r if all(f['exponent']%3==0 or not bad(int(f['base'])) for f in m['factors'])]
print('factors',r[0]['factors'],'count',len(g),'good',g)