Problem:


Score: 300 points

Problem Statement

Find the minimum prime number greater than or equal to X.

Notes

A prime number is an integer greater than 1 that cannot be evenly divided by any positive integer except 1 and itself.

For example, 2, 3, and 5 are prime numbers, while 4 and 6 are not.

Constraints

 2 \le X \le 10^5 

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X

Output

Print the minimum prime number greater than or equal to X.

Sample Input 1

20

Sample Output 1

23

The minimum prime number greater than or equal to 20 is 23.

Sample Input 2

2

Sample Output 2

2

X itself can be a prime number.

Sample Input 3

99992

Sample Output 3

100003



Sample input:
20


Sample output:
23

Submission status: Time Limit Exceeded

Solution code:
bigger_prime_list = [55049,55051,55057,55061,55073,55079,55103,55109,55117,55127,55147,55163,55171,55201,55207,55213,55217,55219,55229,55243,55249,55259,55291,55313,55331,55333,55337,55339,55343,55351,55373,55381,55399,55411,55439,55441,55457,55469,55487,55501,55511,55529,55541,55547,55579,55589,55603,55609,55619,55621,55631,55633,55639,55661,55663,55667,55673,55681,55691,55697,55711,55717,55721,55733,55763,55787,55793,55799,55807,55813,55817,55819,55823,55829,55837,55843,55849,55871,55889,55897,55901,55903,55921,55927,55931,55933,55949,55967,55987,55997,56003,56009,56039,56041,56053,56081,56087,56093,56099,56101,56113,56123,56131,56149,56167,56171,56179,56197,56207,56209,56237,56239,56249,56263,56267,56269,56299,56311,56333,56359,56369,56377,56383,56393,56401,56417,56431,56437,56443,56453,56467,56473,56477,56479,56489,56501,56503,56509,56519,56527,56531,56533,56543,56569,56591,56597,56599,56611,56629,56633,56659,56663,56671,56681,56687,56701,56711,56713,56731,56737,56747,56767,56773,56779,56783,56807,56809,56813,56821,56827,56843,56857,56873,56891,56893,56897,56909,56911,56921,56923,56929,56941,56951,56957,56963,56983,56989,56993,56999,57037,57041,57047,57059,57073,57077,57089,57097,57107,57119,57131,57139,57143,57149,57163,57173,57179,57191,57193,57203,57221,57223,57241,57251,57259,57269,57271,57283,57287,57301,57329,57331,57347,57349,57367,57373,57383,57389,57397,57413,57427,57457,57467,57487,57493,57503,57527,57529,57557,57559,57571,57587,57593,57601,57637,57641,57649,57653,57667,57679,57689,57697,57709,57713,57719,57727,57731,57737,57751,57773,57781,57787,57791,57793,57803,57809,57829,57839,57847,57853,57859,57881,57899,57901,57917,57923,57943,57947,57973,57977,57991,58013,58027,58031,58043,58049,58057,58061,58067,58073,58099,58109,58111,58129,58147,58151,58153,58169,58171,58189,58193,58199,58207,58211,58217,58229,58231,58237,58243,58271,58309,58313,58321,58337,58363,58367,58369,58379,58391,58393,58403,58411,58417,58427,58439,58441,58451,58453,58477,58481,58511,58537,58543,58549,58567,58573,58579,58601,58603,58613,58631,58657,58661,58679,58687,58693,58699,58711,58727,58733,58741,58757,58763,58771,58787,58789,58831,58889,58897,58901,58907,58909,58913,58921,58937,58943,58963,58967,58979,58991,58997,59009,59011,59021,59023,59029,59051,59053,59063,59069,59077,59083,59093,59107,59113,59119,59123,59141,59149,59159,59167,59183,59197,59207,59209,59219,59221,59233,59239,59243,59263,59273,59281,59333,59341,59351,59357,59359,59369,59377,59387,59393,59399,59407,59417,59419,59441,59443,59447,59453,59467,59471,59473,59497,59509,59513,59539,59557,59561,59567,59581,59611,59617,59621,59627,59629,59651,59659,59663,59669,59671,59693,59699,59707,59723,59729,59743,59747,59753,59771,59779,59791,59797,59809,59833,59863,59879,59887,59921,59929,59951,59957,59971,59981,59999,60013,60017,60029,60037,60041,60077,60083,60089,60091,60101,60103,60107,60127,60133,60139,60149,60161,60167,60169,60209,60217,60223,60251,60257,60259,60271,60289,60293,60317,60331,60337,60343,60353,60373,60383,60397,60413,60427,60443,60449,60457,60493,60497,60509,60521,60527,60539,60589,60601,60607,60611,60617,60623,60631,60637,60647,60649,60659,60661,60679,60689,60703,60719,60727,60733,60737,60757,60761,60763,60773,60779,60793,60811,60821,60859,60869,60887,60889,60899,60901,60913,60917,60919,60923,60937,60943,60953,60961,61001,61007,61027,61031,61043,61051,61057,61091,61099,61121,61129,61141,61151,61153,61169,61211,61223,61231,61253,61261,61283,61291,61297,61331,61333,61339,61343,61357,61363,61379,61381,61403,61409,61417,61441,61463,61469,61471,61483,61487,61493,61507,61511,61519,61543,61547,61553,61559,61561,61583,61603,61609,61613,61627,61631,61637,61643,61651,61657,61667,61673,61681,61687,61703,61717,61723,61729,61751,61757,61781,61813,61819,61837,61843,61861,61871,61879,61909,61927,61933,61949,61961,61967,61979,61981,61987,61991,62003,62011,62017,62039,62047,62053,62057,62071,62081,62099,62119,62129,62131,62137,62141,62143,62171,62189,62191,62201,62207,62213,62219,62233,62273,62297,62299,62303,62311,62323,62327,62347,62351,62383,62401,62417,62423,62459,62467,62473,62477,62483,62497,62501,62507,62533,62539,62549,62563,62581,62591,62597,62603,62617,62627,62633,62639,62653,62659,62683,62687,62701,62723,62731,62743,62753,62761,62773,62791,62801,62819,62827,62851,62861,62869,62873,62897,62903,62921,62927,62929,62939,62969,62971,62981,62983,62987,62989,63029,63031,63059,63067,63073,63079,63097,63103,63113,63127,63131,63149,63179,63197,63199,63211,63241,63247,63277,63281,63299,63311,63313,63317,63331,63337,63347,63353,63361,63367,63377,63389,63391,63397,63409,63419,63421,63439,63443,63463,63467,63473,63487,63493,63499,63521,63527,63533,63541,63559,63577,63587,63589,63599,63601,63607,63611,63617,63629,63647,63649,63659,63667,63671,63689,63691,63697,63703,63709,63719,63727,63737,63743,63761,63773,63781,63793,63799,63803,63809,63823,63839,63841,63853,63857,63863,63901,63907,63913,63929,63949,63977,63997,64007,64013,64019,64033,64037,64063,64067,64081,64091,64109,64123,64151,64153,6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prime_list = [2]
for n in range(3, 55049, 2):
  is_prime = True
  for m in prime_list:
    if n % m == 0:
      is_prime = False
      break
  if is_prime:
    prime_list.append(n)
prime_list.extend(bigger_prime_list)
x = int(input())
for n in prime_list:
  if x <= n:
    print(n)
    break

Submission status: Time Limit Exceeded

Solution code:
x=int(input())
count=0

n=1
while True:
	n+=1
	ans=True
	for i in range(2,int(x**0.5)):
		if n%i==0:
			ans=False
	if ans and n>=x:
		print(n)
		break

Submission status: Time Limit Exceeded

Solution code:
def isPrime(x):
    if x <= 1: return False
    i = 2
    while i ** 2 <= x:
        if x % i == 0: return False
        i += 1

a = int(input())
while True:
    a += 1
    if isPrime(a):
        print(a)
        break

Submission status: Time Limit Exceeded

Solution code:
def isPrime(x):
    if x <= 1: return False
    i = 2
    while i ** 2 <= x:
        if x % i == 0: return False
        i += 1

a = int(input())
while True:
    a += 1
    if isPrime(a): print(a)

Submission status: Time Limit Exceeded

Solution code:
N = int(input())
x = 0
while x == 0:
    num = 2
    while N % 2 != 0:
        num += 1
    if num == N:
        x = 1
    else:
        N += 1
print(N)

Submission status: Time Limit Exceeded

Solution code:
X = int(input())

sosu = [2]

for i in range(3, 10**5+100, 2):
    if(all(i % num != 0 for num in sosu)):
        sosu.append(i)   
        if(i >= X):
            print(i if X > 2 else 2)
            break

Submission status: Time Limit Exceeded

Solution code:
X = int(input())
pn=[2]
for L in range(3, 2*X):
    chk=True
    for L2 in pn:
        if L%L2 == 0:chk=False
    if chk==True:pn.append(L)

for i in range(len(pn)):
    if pn[i]>X:
        print(pn[i])
        break
    elif pn[i]==X:
        print(X)
        break

Submission status: Time Limit Exceeded

Solution code:
x = int(input())

s =[2]
a = x

if x==2:
    print(x)
else:
  for i in range(3,2*x,2):
    if all(i%k!=0 for k in s):
        s.append(i)
        if i >=x:
          print(i)
          exit()

Submission status: Time Limit Exceeded

Solution code:
x = int(input())

s =[2]
a = x

if x==2:
    print(x)
else:
  for i in range(3,x,2):
    if all(i%k!=0 for k in s):
        s.append(i)
        
  for t in range(x,2*x):
    if all(t%k!=0 for k in s):
      print(t)
      exit()

Submission status: Time Limit Exceeded

Solution code:
x=int(input())
p=x**0.5
while any(x%i==0 for i in range(2,x//1+1)):
  x+=1
else:
  print(x)

Submission status: Time Limit Exceeded

Solution code:
import sys
input=sys.stdin.readline
X = int(input())
prime = [2]
if X == 2:
    print(2)
else:
    for i in range(2,X):
        c = 0
        for j in prime:
            if i % j == 0:
                c = 1
                break
        if c == 0:
            prime.append(i)
    for i in range(X,X + 1000):
        c = 0
        for j in prime:
            if i % j == 0:
                c = 1
                break
        if c == 0:
            print(i)
            break

Submission status: Time Limit Exceeded

Solution code:

#約数リスト
import math
#素数列挙
def get_primes(limit):
    A = [i for i in range(2, limit+1)]
    P = []
    time = 0
    
    while True:
        prime = min(A)
        
        if prime > math.sqrt(limit):
            break
            
        P.append(prime)
            
        i = 0
        while i < len(A):
            if A[i] % prime == 0:
                A.pop(i)
                continue
            i += 1
            
    for a in A:
        P.append(a)
            
    return P




def resolve():
    n = int(input())
    A = get_primes(int(1.2*n))

    for i in A:
        if i>=n:
            print(i)
            return





if __name__ == "__main__":
    resolve()

Submission status: Time Limit Exceeded

Solution code:

#約数リスト
import math
#素数列挙
def get_primes(limit):
    A = [i for i in range(2, limit+1)]
    P = []
    time = 0
    
    while True:
        prime = min(A)
        
        if prime > math.sqrt(limit):
            break
            
        P.append(prime)
            
        i = 0
        while i < len(A):
            if A[i] % prime == 0:
                A.pop(i)
                continue
            i += 1
            
    for a in A:
        P.append(a)
            
    return P




def resolve():
    n = int(input())
    A = get_primes(2*n)

    for i in A:
        if i>=n:
            print(i)
            return





if __name__ == "__main__":
    resolve()

Submission status: Time Limit Exceeded

Solution code:
X=int(input())
s=[2]
x=2
while x<=10**5+130:
    turn=0
    for i in s:
        if (x%i)==0:
            x+=1
            turn=1
            break
    if turn==0:
        s.append(x)
        x+=1
for i in range(X,10**5+4):
    if i in s:
        print(i)
        break

Submission status: Time Limit Exceeded

Solution code:
import math

x = int(input())

primes = []

for n in range(2, 10000000000, 2):
    f = True
    mp = math.ceil(math.sqrt(n))
    for p in primes:
        if p > mp:
            break
        if n % p == 0:
            f = False
            break
    if f:
        primes.append(n)
        if n >= x:
            print(n)
            exit(0)

Submission status: Time Limit Exceeded

Solution code:
X = int(input())

def notco(x, lst):
  for i in range(len(lst)):
    if x % lst[i] == 0:
      return False
  return True

def minp(x):
  primes = [2]
  i = 3
  while(primes[len(primes)-1] < x):
    if notco(i, primes):
      primes.append(i)
    i += 1
  return primes[len(primes)-1]

print(minp(X))

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-
"""
Created on Wed Mar  4 19:06:03 2020

@author: Kanaru Sato
"""
import math

X = int(input())

target = X
flag = 0

while flag == 0:
    rootX = int(math.sqrt(X))
    for i in range(2, rootX+1):
        if X%i == 0:
            if X%2 == 0:
                X += 1
                break
            else:
                X += 2
                break
        elif i == rootX:
            flag = 1
            break
        else:
            continue

print(X)

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-
"""
Created on Wed Mar  4 19:06:03 2020

@author: Kanaru Sato
"""
import math

X = int(input())

target = X
flag = 0

while flag == 0:
    for i in range(2, int(math.sqrt(X))+1):
        if X%i == 0:
            if X%2 == 0:
                X += 1
                break
            else:
                X += 2
                break
        elif i == int(math.sqrt(X)):
            flag = 1
            break
        else:
            continue

print(X)

Submission status: Time Limit Exceeded

Solution code:
# -*- coding: utf-8 -*-
"""
Created on Wed Mar  4 19:06:03 2020

@author: Kanaru Sato
"""
import math

X = int(input())

target = X
flag = 0

while flag == 0:
    for i in range(2, int(math.sqrt(X))+1):
        if X%i == 0:
            X += 1
            break
        elif i == int(math.sqrt(X)):
            flag = 1
            break
        else:
            continue

print(X)