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

Solution (Python):
x = int(input())
prime_list = []
for n in range(2, 55049):
  is_prime = True
  for m in prime_list:
    if n % m == 0:
      is_prime = False
      break
  if is_prime:
    if x <= n:
      print(n)
      exit(0)
    prime_list.append(n)
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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2401,92413,92419,92431,92459,92461,92467,92479,92489,92503,92507,92551,92557,92567,92569,92581,92593,92623,92627,92639,92641,92647,92657,92669,92671,92681,92683,92693,92699,92707,92717,92723,92737,92753,92761,92767,92779,92789,92791,92801,92809,92821,92831,92849,92857,92861,92863,92867,92893,92899,92921,92927,92941,92951,92957,92959,92987,92993,93001,93047,93053,93059,93077,93083,93089,93097,93103,93113,93131,93133,93139,93151,93169,93179,93187,93199,93229,93239,93241,93251,93253,93257,93263,93281,93283,93287,93307,93319,93323,93329,93337,93371,93377,93383,93407,93419,93427,93463,93479,93481,93487,93491,93493,93497,93503,93523,93529,93553,93557,93559,93563,93581,93601,93607,93629,93637,93683,93701,93703,93719,93739,93761,93763,93787,93809,93811,93827,93851,93871,93887,93889,93893,93901,93911,93913,93923,93937,93941,93949,93967,93971,93979,93983,93997,94007,94009,94033,94049,94057,94063,94079,94099,94109,94111,94117,94121,94151,94153,94169,94201,94207,94219,94229,94253,94261,94273,94291,94307,94309,94321,94327,94331,94343,94349,94351,94379,94397,94399,94421,94427,94433,94439,94441,94447,94463,94477,94483,94513,94529,94531,94541,94543,94547,94559,94561,94573,94583,94597,94603,94613,94621,94649,94651,94687,94693,94709,94723,94727,94747,94771,94777,94781,94789,94793,94811,94819,94823,94837,94841,94847,94849,94873,94889,94903,94907,94933,94949,94951,94961,94993,94999,95003,95009,95021,95027,95063,95071,95083,95087,95089,95093,95101,95107,95111,95131,95143,95153,95177,95189,95191,95203,95213,95219,95231,95233,95239,95257,95261,95267,95273,95279,95287,95311,95317,95327,95339,95369,95383,95393,95401,95413,95419,95429,95441,95443,95461,95467,95471,95479,95483,95507,95527,95531,95539,95549,95561,95569,95581,95597,95603,95617,95621,95629,95633,95651,95701,95707,95713,95717,95723,95731,95737,95747,95773,95783,95789,95791,95801,95803,95813,95819,95857,95869,95873,95881,95891,95911,95917,95923,95929,95947,95957,95959,95971,95987,95989,96001,96013,96017,96043,96053,96059,96079,96097,96137,96149,96157,96167,96179,96181,96199,96211,96221,96223,96233,96259,96263,96269,96281,96289,96293,96323,96329,96331,96337,96353,96377,96401,96419,96431,96443,96451,96457,96461,96469,96479,96487,96493,96497,96517,96527,96553,96557,96581,96587,96589,96601,96643,96661,96667,96671,96697,96703,96731,96737,96739,96749,96757,96763,96769,96779,96787,96797,96799,96821,96823,96827,96847,96851,96857,96893,96907,96911,96931,96953,96959,96973,96979,96989,96997,97001,97003,97007,97021,97039,97073,97081,97103,97117,97127,97151,97157,97159,97169,97171,97177,97187,97213,97231,97241,97259,97283,97301,97303,97327,97367,97369,97373,97379,97381,97387,97397,97423,97429,97441,97453,97459,97463,97499,97501,97511,97523,97547,97549,97553,97561,97571,97577,97579,97583,97607,97609,97613,97649,97651,97673,97687,97711,97729,97771,97777,97787,97789,97813,97829,97841,97843,97847,97849,97859,97861,97871,97879,97883,97919,97927,97931,97943,97961,97967,97973,97987,98009,98011,98017,98041,98047,98057,98081,98101,98123,98129,98143,98179,98207,98213,98221,98227,98251,98257,98269,98297,98299,98317,98321,98323,98327,98347,98369,98377,98387,98389,98407,98411,98419,98429,98443,98453,98459,98467,98473,98479,98491,98507,98519,98533,98543,98561,98563,98573,98597,98621,98627,98639,98641,98663,98669,98689,98711,98713,98717,98729,98731,98737,98773,98779,98801,98807,98809,98837,98849,98867,98869,98873,98887,98893,98897,98899,98909,98911,98927,98929,98939,98947,98953,98963,98981,98993,98999,99013,99017,99023,99041,99053,99079,99083,99089,99103,99109,99119,99131,99133,99137,99139,99149,99173,99181,99191,99223,99233,99241,99251,99257,99259,99277,99289,99317,99347,99349,99367,99371,99377,99391,99397,99401,99409,99431,99439,99469,99487,99497,99523,99527,99529,99551,99559,99563,99571,99577,99581,99607,99611,99623,99643,99661,99667,99679,99689,99707,99709,99713,99719,99721,99733,99761,99767,99787,99793,99809,99817,99823,99829,99833,99839,99859,99871,99877,99881,99901,99907,99923,99929,99961,99971,99989,99991,100003]
for n in bigger_prime_list:
  if x <= n:
    print(n)
    break

Solution (Python):
x = int(input())

def is_prime(x):
    while True:
        for i in range(2, x):
            if x % i == 0:
                return False
        return True

while True:
    if is_prime(x):
        print(x)
        break
    else:
        x += 1

Solution (Python):
import numpy as np

def is_prime(n):
    if n == 1: return False

    for k in range(2, int(np.sqrt(n)) + 1):
        if n % k == 0:
            return False

    return True

x = int(input())

for i in range(10**5):
  if is_prime(x+i) == True:
    print(x+i)
    break

Solution (Python):
import math
def isPrime(n):
  if n == 1: return False

  for k in range(2, int(math.sqrt(n)) + 1):
    if n % k == 0:
      return False
  return True

x = int(input())

for i in range(10**5):
  if isPrime(x+i):
    print(x+i)
    break

Solution (Python):
import math

X=int(input())

def judge(x):
    judge=True
    h=int(math.sqrt(x))
    for i in range(2,h+1):
        r=x%i
        if r==0:
            judge=False
            break
    
    return judge

ans=X
while True:
    if judge(ans):
        print(ans)
        break
    else:
        ans+=1

Solution (Python):
n = int(input())

import math
def prime(n):
  a = math.ceil(math.sqrt(n))
  for i in range(2,a):
    if n%i==0: return 1
  return 0

while (1):
  if prime(n)==0: 
    print(n)
    exit()
  n+=1

Solution (Python):
import math

def is_prime(x):
    if x < 2: return False  
    if x == 2 or x == 3 or x == 5: return True  
    if x % 2 == 0 or x % 3 == 0 or x % 5 == 0: return False  
    prime = 7
    step = 4
    while prime <= math.sqrt(x):
        if x % prime == 0: return False
        prime += step
        step = 6 - step
    return True

def main():
    X = int(input())
    while 1:
        if is_prime(X):
            print(X)
            break
        X += 1


if __name__ == '__main__':
    main()

Solution (Python):
X = int(input())

def is_prime(n):
  for i in range(2,int(n**0.5)+1):
    if n%i == 0:
      return False
  return True

for i in range(X,100000000):
  if is_prime(i) == True:
    print(i)
    break

Solution (Python):
x = int(input())
n = x
while True:
  for i in range(2, n):
    if n%i==0:
      break
  else:
    print(n)
    break
  n+=1

Solution (Python):
X=int(input())
ans=0
for i in range(X,10**8):
    f=0
    for n in range(2,i):
        if i%n==0:
            f+=1
            break
    if f==0:
        ans=i
        break
print(ans)

Solution (Python):
x = int(input())

import random


def is_prime3(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


while True:
    if is_prime3(x):
        print(x)
        exit()
    x += 1

Solution (Python):
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(10 ** 7)

import math
from bisect import bisect_left

def eratosthenes(limit):
    limit += 10 ** 3
    A = [i for i in range(2, limit + 1)]
    P = []

    for i in range(limit):
        prime = min(A)

        if prime > math.sqrt(limit):
            break

        P.append(prime)
        for j in range(limit):
            if j >= len(A):
                break
            if A[j] % prime == 0:
                A.pop(j)
                continue

    for a in A:
        P.append(a)

    return P


x = int(readline())
ans = eratosthenes(x)
print(ans[bisect_left(ans, x)])

Solution (Python):
X = int(input())
while True:
  L = []
  for i in range(1, int(X ** 0.5) + 1):
    if X % i == 0:
      L.append(i)
      if i != X // i:
        L.append(X // i)
  if L == [1, X]:
    print(X)
    exit()
  else:
    X += 1

Solution (Python):
x = int(input())
flag = 0

for i in range(x, x + 1000):
    for j in range(2, x):
        if i%j == 0:
            flag = 1
            break
    if flag == 0:
        print(i)
        exit()
    else:
        flag = 0

Solution (Python):
import math
X = int(input())
Y = int(math.sqrt(X))
while True:
    flg=True
    for i in range(2, Y):
        if X%i!=0:
            continue
        flg=False
        break
    if flg:
        print(X)
        break
    else:
        X+=1
        continue

Solution (Python):
X = int(input())

while True:
    flg=True
    for i in range(2, X):
        if X%i!=0:
            continue
        flg=False
        break
    if flg:
        print(X)
        break
    else:
        X+=1
        continue

Solution (Python):
import math

def isPrime(a):
  for i in range(2,int(math.sqrt(a))+1):
    if a%i==0:
      return False
  return True

x=int(input())

while(not isPrime(x)):
  x+=1

print(x)

Solution (Python):
def isPrime(x):
    if x < 2:
        return False
    for i in range(2, int(pow(x, 0.5)+1)):
        if x%i==0:
            return False
    return True

X = int(input())

while True:
    if isPrime(X):
        print(X)
        break
    else:
        X += 1

Solution (Python):

import math
x = int(input())
n = 10 ** 10
for i in range(x, n):
    for k in range(2, x):
        if i % k == 0:
            break
    else:
        print(i)
        exit()

Solution (Python):
X = int(input())
flag = 0

while flag ==0:
	if X==2:
		X+=1
		break
	for i in range(X-2):
		if X%(i+2)==0:
			break
		if i+3==X:
			flag = 1
			break
	X +=1

print(X-1)

Solution (Python):
x = int(input())
for i in range(x, 100003 + 1):
    for j in range(2, i):
        if i % j == 0:
            break
    else:
        print(i)
        break

Solution (Python):
x = int(input())
p = [True] * 100004
p[0] = False
p[1] = False
for i in range(int(100003 ** 0.5)):
    if p[i] == False:
        continue
    for j in range(2, 100003 // i + 1):
        p[i * j] = False
for i in range(x, 100004):
    if p[i] == True:
        print(i)
        break

Solution (Python):
X = int(input())

def isPrime(x):
    if x <= 1: 
        return False

    for i in range (2, int(x**(1/2)) + 1):
        if x%i == 0:
            return False

    return True

p = X

while isPrime(p) != True:
    p += 1

print(p)

Solution (Python):
import numpy as np
import math
x = int(input())
prime = True
while prime:
    flag = 0
    for j in range(2,math.ceil(np.sqrt(x))):
        if x%j == 0:
            flag = 1
            break
    if flag ==0:
        prime = False
        
    else:
        x+=1
            
print(x)