#!/usr/bin/env sage

import sys
from sage.all import *

# The prime order of libsnark's BN128 curve
r = 21888242871839275222246405745257275088548364400416034343698204186575808495617
F = GF(r)

count = 0
primecount = 0
done = False
while not done:
    b = F.random_element()
    try:
	E = EllipticCurve(F, [-3, b])
	Ec = E.cardinality()
	count += 1
	print "b =", b, "Ec =", Ec, "c =", count, "pc =", primecount
	Etc = 2 * r + 2 - Ec
	if Ec in Primes():
	    primecount += 1
	    print "Ec is prime; primecount =", primecount
	    if Etc in Primes():
		print "Solution found:", b
		done = True
    except KeyboardInterrupt:
	print "Terminating on keyboard interrupt"
	sys.exit(1)
    except:
    	pass