My Mersenne Primality Testing Algorithm

I'm not sure how fast it is compared to GIMPS, but it is acurate for all Mersenne or Fermat primes. See my article Value-Counting Up to N for why.

import sys
import time

# Remove the limit
sys.set_int_max_str_digits(0)

i = 0

def signal_handler(sig, frame):
	global i
	if sig == signal.SIGINT:
		print("index = %i" % (i))
	sys.exit(0)

def int_sqrt(n):
	"""
	Calculate the integer square root of a non-negative integer n.
	This function returns the largest integer whose square is less than or equal to n.
	"""
	if n < 0:
		raise ValueError("Cannot calculate square root of a negative number.")
	if n == 0:
		return 0
	x = n
	y = 1
	i = 0
	while x > y:
		x = (x + y) // 2
		y = n // x
	return x

def prime_power(n):
	signal.signal(signal.SIGINT, signal_handler)
	total = 0
	half_n = (n + 1) // 2
#	limit = half_n
#	limit = math.ceil((half_n*(half_n + 1) // 2 + 1) / n)
	limit = (n + 13)//8
	start_time = time.perf_counter()
	end_time = start_time

	global i
	for i in range(2, limit):
		# border_value represents the number that ends on the last
		# column when all numbers up to it are added and wrapped.
		border_value = int((int_sqrt(8 * i * n + 1) - 1)/2)
		total = (border_value * (border_value + 1)//2)
		elapsed_time = end_time - start_time
		if (total == (i * n)):# or (total + (border_value + 1)//2 == (i * n)):
			print("%i" % (border_value))
			return
		end_time = time.perf_counter()
		elapsed_time = end_time - start_time
		if elapsed_time > WAIT_TIME:
			start_time = end_time
			end_time = time.perf_counter()
	print("\tprime_power")

print("p\tborder\tprime power")

prime_power(2**89-1)