Buggy python submission (verdict: Time Limit Exceeded):
import random

def gcd(a,b):
        if b == 0:
                return a
        else:
                return gcd(b , a%b)

def is_prime(q,k=50):
    q = abs(q)
    if q == 2: return True
    if q < 2 or q&1 == 0: return False

    d = (q-1)>>1
    while d&1 == 0:
        d >>= 1
    
    for i in range(k):
        a = random.randint(1,q-1)
        t = d
        y = pow(a,t,q)
        while t != q-1 and y != 1 and y != q-1: 
            y = pow(y,2,q)
            t <<= 1
        if y != q-1 and t&1 == 0:
            return False
    return True
 
a, b = map(int,input().split())
 
c = 1
m = gcd(a,b)
for i in range(1,m+1):
	if a % i == 0 and b % i == 0:
		if is_prime(i):
			c+=1
print(c)

Fixed submission:
import random

def gcd(a,b):
        if b == 0:
                return a
        else:
                return gcd(b , a%b) 
def is_prime(q,k=50):
    q = abs(q)
    if q == 2: return True
    if q < 2 or q&1 == 0: return False

    d = (q-1)>>1
    while d&1 == 0:
        d >>= 1

    for i in range(k):
        a = random.randint(1,q-1)
        t = d
        y = pow(a,t,q)
        while t != q-1 and y != 1 and y != q-1:
            y = pow(y,2,q)
            t <<= 1
        if y != q-1 and t&1 == 0:
            return False
    return True

a, b = map(int,input().split())

c = 1
m = gcd(a,b)

i = 1
while i * i <=m:
        if a%i == 0 and b%i == 0:
                if is_prime(i):
                        c+=1
                if is_prime(m//i):
                        c+=1
        i+=1
print(c)

Buggy python submission (verdict: Time Limit Exceeded):
import random
def is_prime(q,k=50):
    q = abs(q)
    if q == 2: return True
    if q < 2 or q&1 == 0: return False

    d = (q-1)>>1
    while d&1 == 0:
        d >>= 1
    
    for i in range(k):
        a = random.randint(1,q-1)
        t = d
        y = pow(a,t,q)
        while t != q-1 and y != 1 and y != q-1: 
            y = pow(y,2,q)
            t <<= 1
        if y != q-1 and t&1 == 0:
            return False
    return True
 
a, b = map(int,input().split())
 
c = 1
for i in range(1,min(a,b)+1):
	if a % i == 0 and b % i == 0:
		if is_prime(i):
			c+=1			
		
print(c)

Fixed submission:
import random

def gcd(a,b):
        if b == 0:
                return a
        else:
                return gcd(b , a%b) 
def is_prime(q,k=50):
    q = abs(q)
    if q == 2: return True
    if q < 2 or q&1 == 0: return False

    d = (q-1)>>1
    while d&1 == 0:
        d >>= 1

    for i in range(k):
        a = random.randint(1,q-1)
        t = d
        y = pow(a,t,q)
        while t != q-1 and y != 1 and y != q-1:
            y = pow(y,2,q)
            t <<= 1
        if y != q-1 and t&1 == 0:
            return False
    return True

a, b = map(int,input().split())

c = 1
m = gcd(a,b)

i = 1
while i * i <=m:
        if a%i == 0 and b%i == 0:
                if is_prime(i):
                        c+=1
                if is_prime(m//i):
                        c+=1
        i+=1
print(c)

Buggy python submission (verdict: Time Limit Exceeded):
import math
def is_prime(n):
	if n == 1: return True
	for k in range(2, int(math.sqrt(n)) + 1):
		if n % k == 0:
			return False
	return True

a, b = map(int,input().split())

c = 0
for i in range(1,min(a,b)+1):
	if a % i == 0 and b % i == 0:
		if is_prime(i):
			c+=1			
		#cd_n.append(i)
print(c)

Fixed submission:
import random

def gcd(a,b):
        if b == 0:
                return a
        else:
                return gcd(b , a%b) 
def is_prime(q,k=50):
    q = abs(q)
    if q == 2: return True
    if q < 2 or q&1 == 0: return False

    d = (q-1)>>1
    while d&1 == 0:
        d >>= 1

    for i in range(k):
        a = random.randint(1,q-1)
        t = d
        y = pow(a,t,q)
        while t != q-1 and y != 1 and y != q-1:
            y = pow(y,2,q)
            t <<= 1
        if y != q-1 and t&1 == 0:
            return False
    return True

a, b = map(int,input().split())

c = 1
m = gcd(a,b)

i = 1
while i * i <=m:
        if a%i == 0 and b%i == 0:
                if is_prime(i):
                        c+=1
                if is_prime(m//i):
                        c+=1
        i+=1
print(c)