Buggy python submission (verdict: Runtime Error):
from functools import reduce
import random
import time

sTime = time.time()
N = int(input())
A = [int(input()) for _ in range(N+1)][::-1]

def gcd(a, b):
    b = abs(b)
    while b != 0:
        r = a%b
        a,b = b,r
    return a
def f(n):
    ret = A[N]
    for i in range(N-1, -1, -1):
        ret = ret * n + A[i]
    return ret

ans = 0
while time.time()-sTime < 1.5:
    k = random.randrange(10**5)
    ans = gcd(ans, f(k))

def primeFactor(N):
    i = 2
    ret = {}
    n = N
    if n < 0:
        ret[-1] = 1
        n = -n
    if n == 0:
        ret[0] = 1
    d = 2
    sq = int(n ** (1/2))
    while i <= sq:
        k = 0
        while n % i == 0:
            n //= i
            k += 1
            ret[i] = k
        if k > 0:
            sq = int(n**(1/2))
        if i == 2:
            i = 3
        elif i == 3:
            i = 5
        elif d == 2:
            i += 2
            d = 4
        else:
            i += 4
            d = 2
        
    if n > 1:
        ret[n] = 1
    return ret

for i in primeFactor(ans):
    print(i)



Fixed submission:
from functools import reduce
import random
import time
MOD = 59490679579998635868564022242503445659680322440679327938309703916140405638383434744833220555452130558140772894046169700747186409941317550665821619479140098743288335106272856533978719769677794737287419461899922456614256826709727133515885581878614846298251428096512495590545989536239739285290509870860732435109794045491640561011775744617218426011793283330497878491137999673760740717904979730106994180691956740996319139767941335979146924614249205862051182094081815447356600355657858936442589201739350474320966093143098768914226528498860747050474426418211313776073365498029087492308102876323562641651940555529817223923967479711293692697592800750806084802623966596666156361791014935954720420383555300213829134029560826306201326905674141090667002959274513478562033467485802590354539887133866434256562999666615074220857502563011098759348850149774083443643246907501430076141377431759984926248272553982527014011245310690986644461251576837779050124866641531488351016070300247918750613207952783437248236577750579092103591540592540838395240861443615842939673889972504776455114767522430347610500271801944701491874649306605557851914677316523034726044356368337787113190245601235705959816327016988315321850324065292964680148884818699916224411245926491625245571963741062587277736372090007125908660590314049976206281064703285728879581199596401313352724403492043120507597057004633720111008838673185885941472392623805512709896864520875740497617898566981218781313900004406341154884180472153171064617953661517880143988867189622824081729539392205701820144922307223627345876707465251206005262622236311161449785941834002795854996108322186230425179217618301526151712928790928933798369678844576216735378555233905935973195721247604933753363412045618703247367192610615234835041956551569232557323060407648325565048712478527583315981204846341857095134567470182330491262285172727037299211391244340592936174221176781260586188162350081192408213470101717320475998863222409777310443027421196981193126541663212124245716187453863438039402316877152286468198891603632606578778749292403571792687832081974134637014026451921536576338243322267400651083805535119025415817887075652758045539565968044552126338330231434466204888993650859153585380124240540573308417330478048240203241631072371322849430883727355239704116556046700749530006852187064160849175332758172150251213637470549781080491037088372092203085237973008861896576796238915011886636658033019385943299986285181723378096425117379056207797455963451889971988904466449319007760192467211209692128894691704353648198130409333996534250878389064152054828983825841234644875996912485916827004219887033833599723481903489316488764021700996686817244736947119285629049355809027206179193628292018441744552168286541735687924729198455883895791600170372255284216915442808139396541702893732917062958054499525549626455191658842064247047426187897146172971001949767308335268505414284088528125611263685734457560292833389995980698745893243832547007166243476192958601735336260255598581701267151224204461879782815468518040925292817115377696676461775120750971210951527384637825092221708015393564320979357698186262039029460777050248162599194429941464248920952161182024344007059684970270762248243899640259750891406957836740989312390963091260380990901672119736141666856448171380781556117025832312710039041398538035351795267732240730608951176127282191528457681241590895740457571038936173983449289126574141189374690274057472401359482497502067814596008557725079835212621242944853319496441084441343866446380876967613370281793088540430288658573281302876742323336651987699532240686371751448290351615451932054274752105688318766958111191822471878078268490672607804265064578569581247796205593441336042254502454646980009177290888726099355974892680373341371214123450598691915802122913613669446370194221846225597401405625536693874723700374068542217340621938985167525416725638580266200550048001242788847319217369432802469735271132107428204697172144851088692772696511622350096452418244968500432645305761138012204888798724453956720733374364721511323104353496583927094760495687785031050687852300161433757934364774351673531859394855389527851678630166084819717354779333605871648837631164630550613112327670353108353791304451834904017538583880634608113426156225757314283269948216017294095002859515842577481167417167637534527111130468710
sTime = time.time()

def gcd(a, b):
    b = abs(b)
    while b != 0:
        r = a%b
        a,b = b,r
    return a
def gcd_mult(numbers):
    return reduce(gcd, numbers)

N = int(input())
A = [int(input()) for _ in range(N+1)][::-1]
g = gcd_mult(A)

A = [a//g for a in A]

def f(n):
    ret = A[N]
    for i in range(N-1, -1, -1):
        ret = (ret * n + A[i]) % MOD
    return ret

ans = MOD
while time.time()-sTime < 1.5:
    k = random.randrange(10**10)
    ans = gcd(ans, f(k))

def primeFactor(N):
    i = 2
    ret = {}
    n = N
    if n < 0:
        ret[-1] = 1
        n = -n
    if n == 0:
        ret[0] = 1
    d = 2
    sq = int(n ** (1/2))
    while i <= sq:
        k = 0
        while n % i == 0:
            n //= i
            k += 1
            ret[i] = k
        if k > 0:
            sq = int(n**(1/2))
        if i == 2:
            i = 3
        elif i == 3:
            i = 5
        elif d == 2:
            i += 2
            d = 4
        else:
            i += 4
            d = 2
        
    if n > 1:
        ret[n] = 1
    return ret
ANS = []
for i in primeFactor(ans*g):
    ANS.append(i)

ANS = sorted(ANS)
for ans in ANS:
    print(ans)