The prime numbers are not regularly spaced. For example from `2` to `3` the gap is `1`.
From `3` to `5` the gap is `2`. From `7` to `11` it is `4`.
Between 2 and 50 we have the following pairs of 2-gaps primes:
`3-5, 5-7, 11-13, 17-19, 29-31, 41-43`

A prime gap of length n is a run of n-1 consecutive composite numbers between two **successive** primes (see: http://mathworld.wolfram.com/PrimeGaps.html).

We will write a function gap with parameters:

`g` (integer >= 2) which indicates the gap we are looking for

`m` (integer > 2) which gives the start of the search (m inclusive)

`n` (integer >= m) which gives the end of the search (n inclusive)

In the example above `gap(2, 3, 50)` will return `[3, 5] or (3, 5) or {3, 5}` which is the first pair between 3 and 50 with a 2-gap.

So this function should return the **first** pair of two prime numbers spaced with a gap of `g`
between the limits `m`, `n` if these numbers exist otherwise `nil or null or None or Nothing` (depending on the language). 

In C++ return in such a case `{0, 0}`. In F# return `[||]`. In Kotlin return `[]`

#Examples:
`gap(2, 5, 7) --> [5, 7] or (5, 7) or {5, 7}`

`gap(2, 5, 5) --> nil. In C++ {0, 0}. In F# [||]. In Kotlin return `[]`

`gap(4, 130, 200) --> [163, 167] or (163, 167) or {163, 167}`

([193, 197] is also such a 4-gap primes between 130 and 200 but it's not the first pair)

`gap(6,100,110) --> nil or {0, 0}` : between 100 and 110 we have `101, 103, 107, 109` but `101-107`is not a
6-gap because there is `103`in between and `103-109`is not a 6-gap because there is `107`in between.

# Note for Go
For Go: nil slice is expected when there are no gap between m and n.
Example: gap(11,30000,100000) --> nil

#Ref
https://en.wikipedia.org/wiki/Prime_gap

Difficulty: introductory

Starter code:

def gap(g, m, n):
	

Solutions:
def gap(g, m, n):
    previous_prime = n
    for i in range(m, n + 1):
        if is_prime(i):
            if i - previous_prime == g: 
                return [previous_prime, i]
            previous_prime = i
    return None
            
    
def is_prime(n):
    for i in range(2, int(n**.5 + 1)):
        if n % i == 0:
            return False
    return True

def gap(g, m, n):
    prev = 2
    for x in range(m|1, n + 1, 2):
        if all(x%d for d in range(3, int(x**.5) + 1, 2)):
            if x - prev == g: return [prev, x]
            prev = x

import numpy as np

sieve = np.ones(12_000_000, dtype=bool)
sieve[0] = sieve[1] = 0
sieve[2*2::2] = 0
for i in range(3, int(len(sieve)**0.5)+1, 2):
    if sieve[i]:
        sieve[i*i::i] = 0
primes = np.array([i for i, x in enumerate(sieve) if x], dtype=int)

def gap(g, m, n):
    i = primes.searchsorted(m)
    j = primes.searchsorted(n)
    for k in range(i, j+1):
        if primes[k+1] - primes[k] == g:
            return list(primes[k:k+2])

def is_prime(a):
    return all(a % i for i in range(2, int(a**0.5)+1))
        
def gap(g, m, n):
    for a in range(m, n-g+1):
        if is_prime(a) and is_prime(a+g) and not any(is_prime(j) for j in range(a+1, a+g)):
            return [a, a+g]


def gap(g, m, n):
    prev = None
    for i in range(m if m%2 else m+1, n+1, 2):
        isPrime = True
        for k in range(2, round(i**0.5)+1):
            if i%k == 0:
                isPrime = False
                break
        if isPrime:
            if prev:
                if i-prev == g:
                    return [prev, i]
            prev = i
    return None

def gap(g, m, n):
    for i in range(m, n):
        if isprime(i): # prime
            if isprime(i + g): # prime at gap
                if not any(list([isprime(x) for x in (list(range(i + 1, i + g)))])): # no prime inbetween              
                   return [i, i + g]
        
        
def isprime(x):
    if x <= 1 or x % 2 == 0:
        return False
    d = 3
    while d * d <= x:
        if x % d == 0:
            return False
        d = d + 2
    return True 


def isPrime(x):
    x = int(x)
    if x == 2:
        return True
    if x == 1:
        return False
    if x in (3,5,7):
        return True
    if x % 2 == 0 or x%3 == 0 or x % 5 == 0 or x%7 ==0:
        return False
    for i in range(2,int(x**.5)+1):
         if x % i == 0:  
                return False
    return True

def gap(gap, start, end):
    if start % 2 == 0:
        start += 1
    for i in range(start,end+1,2):
        if i + gap > end:
            break
        if isPrime(i) and isPrime(i+gap):
            good = True
            for j in range(i+1,i+gap):
                if isPrime(j):
                    good = False
                    break
            if good:
                return [i,i+gap]
    return None
                


def gap(g, m, n):
    import math
    simple = []
    numbers = []
    d = 3
    for i in range(m,n+1):
        if i%2==0:
            pass
        else:
            while d*d <=i and  i%d !=0:
                d+=2
            if d*d>i:
                simple.append(i)
                p = math.fabs(i - simple[simple.index(i) - 1])
                if p == g:
                    return [i-g,i]
            d = 3

    return None



def isPrime(x):
    x = int(x)
    if x == 2:
        return True
    if x == 1:
        return False
    if x in (3,5,7):
        return True
    if x % 2 == 0 or x%3 == 0 or x % 5 == 0 or x%7 ==0:
        return False
    for i in range(2,int(x**.5)+1):
         if x % i == 0:  
                return False
    return True

def gap(gap, start, end):
    for i in range(start,end+1):
        if isPrime(i) and isPrime(i+gap) and i+gap <= end:
            good = True
            for j in range(i+1,i+gap):
                if isPrime(j):
                    good = False
                    break
            if good:
                return [i,i+gap]
    return None
                


import math
def prime_test(x):
    for i in range(2,int(math.sqrt(x))+1):
        if x%i==0:
            return 'not_prime'
        else:
            continue
    return 'prime'

def gap(g, m, n):
    current_number=m
    #print('The gap is ' + str(g))
    while True:
        #print(current_number)
        if current_number>n:
            return None
        if prime_test(current_number)=='not_prime':
            #print(str(current_number) + ' is not prime!')
            current_number=current_number+1
        else:
            if prime_test(current_number+g)=='not_prime':
                #print('But '+ str(current_number+g) + ' is not prime!')
                current_number=current_number+1
            else:
                #print(str(current_number+g) + ' is also prime!')
                prime_in_between=0
                for i in range(current_number+2, current_number+g):
                    if prime_test(i)=='prime':
                        #print('But ' + str(i)+ ' is also prime and it is in between! Not good')
                        prime_in_between=i
                        break
                    else:
                        continue
                if prime_in_between==0:
                    return [current_number, current_number+g]
                else:
                    current_number=current_number+1
                    
                

        


def prime(x):
    if x < 3 or not x%2: return x==2
    return all(x%i for i in range(3, int(x**0.5)+1, 2))

D = {}
def gap(g, m, n):
    get = lambda x: D[x] if x in D else D.setdefault(x, prime(x))
    for i in range(m, n-g+1):
        if get(i) and get(i+g) and not any(map(get, range(i+1, i+g))):
            return [i, i+g]

def gap( g, m, n ):
    import math

    np = None
    for i in range( m, n ):
        is_np, e = True, 2
        while e <= math.sqrt( i ) and is_np:
            if i%e == 0:
                is_np = False
            e += 1
        
        if not is_np: 
            continue
        elif np and i - np == g:
            return [np, i]
        else: np = i

    return None

def gap(g, m, n):
    prime_prev = n
    for i in range(m,n+1):
        if prime_yn(i):
            if i-prime_prev==g:
                return [prime_prev,i]
            prime_prev = i
    return None

def prime_yn(x):
    for j in range(2, int(x**0.5+1)):
        if x%j==0:
            return False
    return True


    


def gap(g, m, n):
    from math import sqrt; from itertools import count, islice

    def isPrime(n):
        return n > 1 and all(n%i for i in islice(count(2), int(sqrt(n)-1)))
    
    prime = n
    for i in range(m,n+1):
        if isPrime(i):
            if i - prime == g:
                return [prime, i]
            prime = i
    return None

def is_prime(num):
    square_num =int(num**0.5)+1
    for divisor in range(2,square_num):
        if num % divisor == 0:
            return False
    return True
            
def gap(g, m, n):
    for num in range(m,n+1):
        if (is_prime(num) and is_prime(num+g) 
            and not any(is_prime(num1) for num1 in range(num+1,num+g))):
            return [num,num+g]
            break
    return None
        


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

    return True
def gap(g, m, n):
    for i in range(m,n+1):
        if isPrime(i) and isPrime(i+g) and not any(isPrime(i+j) for j in range(1,g)):
            return [i,i+g]
            


def is_prime(n):
    if n % 2 == 0: return False
    for i in range(3, int(n**0.5) + 1, 2):
        if n % i == 0: return False
    return True

def gap(g, m, n):
    for x in range(m, n+1-g):
        if is_prime(x) and is_prime(x+g) \
            and not any(map(is_prime, range(x+1, x+g))):
            return [x, x+g]

primes = []

def is_prime(a):
    if a in primes: 
        return True
    if a < 2: return False
    for x in range(2, int(a**0.5) + 1):
        if a % x == 0:
            return False
    primes.append(a)
    return True

def gap(g, m, n):
    p0 = 0
    if m % 2 == 0: m += 1
    for i in range(m,n+1,2):
        if is_prime(i):
            if p0 == 0: p0 = i
            elif i-p0 == g: return [p0,i]
            else: p0 = i; continue
    return None


import math
def gap(g,a,b):
    primes=[]
    for n in range(a,b):
        if all(n%i!=0 for i in range(2,int(math.sqrt(n))+1)):
            if primes!=[] and n-primes[-1]==g: return [primes[-1],n]
            primes.append(n)
    return None

def gap(g, m, n):
    first = first_prime(m, n)
    while first:
        next = first_prime(first+1, n)
        if next is not None and (next - first == g):
            return [first, next]
        first = first_prime(first+1, n)
    return None

def first_prime(start, end):
    for num in range(start, end+1):
        for i in range(2, int(num**0.5) + 1):
            if num % i == 0:
                break
        else:
            return num
    return None


import math
def gap(g, m, n):
    gapn = []
    prevprime = 0
    for i in range(m, n + 1):
        for j in range(2, int(math.ceil(i**0.5) + 1)):   
            if (i % j) == 0:
                break
        else:
            if prevprime > 0 and i - prevprime == g:
                gapn.append(prevprime)
                gapn.append(i)
                break
            prevprime = i
    if len(gapn) > 0:
        return gapn
    else:
        return None


def gap(g, m, n):
    def isprime(a):
        a = abs(int(a))
        if a < 2: return False
        if a == 2: return True    
        if not a & 1: return False
        for x in range(3, int(a**0.5)+1, 2):
            if a % x == 0:
                return False
        return True

    if g & 1:
        if 2>=m and 2<=n:
            if isprime(2+g):
                return [2, 2+g]
    else:
        begin = m + (not m&1)
        status = False
        result = []
        for j in range(begin, n, g):
            for i in range(int(g/2)):
                if isprime(j + 2*i):
                    if status:
                        status = False
                        break
                    if isprime(j + 2*i + g):
                        result = [j + 2*i, j + 2*i + g]
                        status = True
                else:
                    if isprime(j + 2*i + g):
                        if not status:
                            break
            if status:
                return result
    return None

def prime (number):
    if number < 2: return False
    elif number == 2: return True
    elif number % 2 == 0: return False
    for i in range(3, int(number ** 0.5) + 1, 2):
        if number % i == 0: return False
    return True
    
def gap(g, m, n):
    res = []
    i = m
    while (i < n + 1):
        if prime(i):
            res.append(i)
            break
        i += 1
    while True:
        j = i + 1
        while (j < n + 1):
            if prime(j):
                if (j - i == g):
                    res.append(j)
                    return res
                else:
                    res[0] = j
                    i = j
            j += 1
        return None

import math
def IsPrime(n):
    n_up = n
    num = 2
    while(num<=n_up):
        
        if n%num:
            num+=1
            n_up = n//num
        else: return False
    return True    
def gap(g,m,n):
    prev_prime=-1
    curr_prime=-1
    while (curr_prime-prev_prime)!=g :
        if IsPrime(m):
            prev_prime = curr_prime
            curr_prime = m
        m+=1
        if(m>=n):
            return None
    return [prev_prime, curr_prime]

def gap(g, m, n):
        x = [n]
        for i in range(m,n+1):
                        if check_prime(i):
                             x.append(i)
                             if len(x)>=2 and x[len(x)-1]-x[len(x)-2]==g:
                                         return [x[len(x)-2],x[len(x)-1]]
                             else:
                                  x.remove(x[len(x)-2])


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

import numpy 

def sieve(n):
    prime = numpy.ones(n//3 + (n%6==2), dtype=numpy.bool)
    for i in range(3, int(n**.5) + 1, 3):
        if prime[i // 3]:
            p = (i + 1) | 1
            prime[p*p//3::2*p] = False
            prime[p*(p-2*(i&1)+4)//3::2*p] = False
    result = (3 * prime.nonzero()[0] + 1) | 1
    result[0] = 3
    return numpy.r_[2,result]

primes = sieve(12*10**6)

def gap(g,m,n): 
    l = 0 
    r = len(primes)-1 
    start = 10**8 
    while l<=r:
        mid = l+(r-l)//2 
        if primes[mid] >= n:
            r = mid-1 
        elif primes[mid] < m: 
            l = mid+1 
            if start == 10**8:
                start = mid 
            else:
                start = max(mid,start) 
        elif m <= primes[mid] <= n:
            start = min(mid,start) 
            r = mid-1 
    
    for i in range(start,len(primes)): 
        if primes[i] > n:
            break
        if primes[i] < m:
            continue 
        if primes[i+1] - primes[i] == g:
            return [primes[i],primes[i+1]]
    return None 

b = 1500000
lp = [0] * (b+1)
pr = []
for i in range(2,b+1):
    if not lp[i]:
        lp[i] = i
        pr.append(i)
    j = 0
    while j < len(pr) and pr[j] <= lp[i] and i*pr[j]<=b:
        lp[i*pr[j]] = pr[j]
        j += 1
pr.append(10000139)
pr.append(10000141)
def gap(g,start,stop):
    for i in range(len(pr)-1):
        if pr[i]+g > stop:
            break
        if start<=pr[i]<=stop and pr[i]+g <= stop:
            if pr[i+1]-pr[i] == g:
                return [pr[i],pr[i+1]]
    return None  

def gap(g, n, m):
    p_prime = None
    for i in range(n, m + 1):
        if all(i % j for j in range(2, int(i ** 0.5) + 1)):
            if p_prime is not None and i - p_prime == g:
                return ([p_prime, i])
            p_prime = i

#standard prime checker algo
def isPrime(n): 
    #corner points
    if (n<=1): 
        return False
    if (n<=3): 
        return True
    if (n%2==0 or n%3==0) : 
        return False
    i = 5
    while(i*i<=n): 
        if(n%i==0 or n%(i+2)==0): 
            return False
        i=i+6
    return True
        
def gap(gap_size, start_srch, end_srch):
    while start_srch<=end_srch:
        if isPrime(start_srch) and isPrime(start_srch+gap_size) and not any(map(isPrime,range(start_srch+1,start_srch+gap_size))):
            return [start_srch,start_srch+gap_size]
        else:
            start_srch += 1
    return None

from math import sqrt
def prime_gen(m, n):
    is_prime = lambda n: all(n % i for i in range(2, int(sqrt(n)+1)))
    for i in range(m, n+1):
        if is_prime(i):
            yield i
def gap(g, m, n):
    z = prime_gen(m, n)
    ini = next(z)
    while True:
        end = next(z, 'fin')
        try:
            if end - ini == g:
                return [ini, end]
            else:
                ini = end
        except:
            return None

def gap(g, m, n):
    def is_prime(num):
        if num < 4: return num > 1
        if num % 6 != 1 and num % 6 != 5: return False
        sqrt = int(num ** 0.5)
        for i in range(5, sqrt + 1, 6):
            if num % i == 0 or num % (i + 2) == 0: return False
        return True

    for i in range(m, n + 1):
        if is_prime(i):
            for j in range(i + 1, n + 1):
                if is_prime(j):
                    if j - i == g:
                        return [i, j]
                    break
                if j == n: return None
    return None

import math

def isprime(y):
    if all(y%i!=0 for i in range(3,int(math.sqrt(y))+1, 2)):
        return True
def gap(g, m, n):
    if m % 2 == 0:
        m = m + 1;
    for num in range(m,n,2):
        if isprime(num) == True:
            for x in range(num+2, num+g+1, 2):
                print(x)
                if isprime(x) == True:
                    print((x,num,g))
                    if x - num == g:
                        return [num, x]
                        break
                    else:
                        break
#OH MY GOD IT ACTUALLY WORKED



                        



from math import sqrt
from itertools import count, islice

def isPrime(n):
    return n > 1 and all(n%i for i in islice(count(2), int(sqrt(n)-1)))

def gap(g, m, n):
    last_prime = None
    for i in range(m, n + 1):
        if isPrime(i):
            if last_prime is not None:
                if i - last_prime == g:
                    return [last_prime, i]
            last_prime = i
    return None
            


def gap(g, m, n):
    
    def is_prime(p):
        if p % 2 == 0: return False
        for i in range(3, int(p**0.5)+1, 2):
            if p % i == 0: return False
        return True

    first = 0
    for t in range(m, n+1):
        #print(t, first)
        if not(is_prime(t)): continue
        #print(t, 'is prime')
        if first == 0:
            first = t
            #print(first, 'is first')
        elif t - first == g:
            return [first, t]
        else:
            first = t
    
#    prime_list = []        
#    for t in range(m, n+1):
#        if is_prime(t): prime_list.append(t)
#    
#    for i in range(len(prime_list) - 1):
#        if prime_list[i+1] - prime_list[i] == g:
#            return [prime_list[i], prime_list[i+1]]
    
    return None

import math

def gap(g, m, n):
    primes = []
    gaps = []
    for num in range(m, n+1):
        max_div = math.floor(math.sqrt(num))
        if sum([num % i == 0 for i in range(2,max_div+1)]) == 0:
            primes.append(num)
            diff = primes[primes.index(num)]-primes[primes.index(num)-1]
            if diff == g:
                return [primes[primes.index(num)-1],primes[primes.index(num)]]

import math
def gap(g, m, n):
    prev = None
    curr = None
    for i in range(m, n + 1):
        if isPrime(i):
            if prev and i - prev == g:
                curr = i
                break
            prev = i  
    if curr:         
        return [prev, curr]
    else:
        return None
    
def isPrime(n):
    if n % 2 == 0 and n > 2: 
        return False
    return all(n % i for i in range(3, int(math.sqrt(n)) + 1, 2))


import functools

@functools.lru_cache(None)
def is_prime(n):    
    if n < 4:
        return True

    for i in range(3, int(n ** .5) + 1):
        if n % i == 0:
            return False
    return True

def gap(g, m, n):
    start = 0
    
    if m % 2 == 0:
        m += 1
    
    for num in range(m, n + 1, 2):
        if is_prime(num):
            if start and num - start == g:
                return [start, num]
            
            start = num


PRIMES = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039,5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827,5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619,6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871,6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997,7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151,7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,7307,7309,7321,7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,7477,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561,7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,7687,7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,7841,7853,7867,7873,7877,7879,7883,7901,7907,7919,7927,7933,7937,7949,7951,7963,7993,8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111,8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243,8263,8269,8273,8287,8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83153,983173,983179,983189,983197,983209,983233,983239,983243,983261,983267,983299,983317,983327,983329,983347,983363,983371,983377,983407,983429,983431,983441,983443,983447,983449,983461,983491,983513,983519,983527,983531,983533,983557,983579,983581,983597,983617,983659,983699,983701,983737,983771,983777,983783,983789,983791,983803,983809,983813,983819,983849,983861,983863,983881,983911,983923,983929,983951,983987,983993,984007,984017,984037,984047,984059,984083,984091,984119,984121,984127,984149,984167,984199,984211,984241,984253,984299,984301,984307,984323,984329,984337,984341,984349,984353,984359,984367,984383,984391,984397,984407,984413,984421,984427,984437,984457,984461,984481,984491,984497,984539,984541,984563,984583,984587,984593,984611,984617,984667,984689,984701,984703,984707,984733,984749,984757,984761,984817,984847,984853,984859,984877,984881,984911,984913,984917,984923,984931,984947,984959,985003,985007,985013,985027,985057,985063,985079,985097,985109,985121,985129,985151,985177,985181,985213,985219,985253,985277,985279,985291,985301,985307,985331,985339,985351,985379,985399,985403,985417,985433,985447,985451,985463,985471,985483,985487,985493,985499,985519,985529,985531,985547,985571,985597,985601,985613,985631,985639,985657,985667,985679,985703,985709,985723,985729,985741,985759,985781,985783,985799,985807,985819,985867,985871,985877,985903,985921,985937,985951,985969,985973,985979,985981,985991,985993,985997,986023,986047,986053,986071,986101,986113,986131,986137,986143,986147,986149,986177,986189,986191,986197,986207,986213,986239,986257,986267,986281,986287,986333,986339,986351,986369,986411,986417,986429,986437,986471,986477,986497,986507,986509,986519,986533,986543,986563,986567,986569,986581,986593,986597,986599,986617,986633,986641,986659,986693,986707,986717,986719,986729,986737,986749,986759,986767,986779,986801,986813,986819,986837,986849,986851,986857,986903,986927,986929,986933,986941,986959,986963,986981,986983,986989,987013,987023,987029,987043,987053,987061,987067,987079,987083,987089,987097,987101,987127,987143,987191,987193,987199,987209,987211,987227,987251,987293,987299,987313,987353,987361,987383,987391,987433,987457,987463,987473,987491,987509,987523,987533,987541,987559,987587,987593,987599,987607,987631,987659,987697,987713,987739,987793,987797,987803,987809,987821,987851,987869,987911,987913,987929,987941,987971,987979,987983,987991,987997,988007,988021,988033,988051,988061,988067,988069,988093,988109,988111,988129,988147,988157,988199,988213,988217,988219,988231,988237,988243,988271,988279,988297,988313,988319,988321,988343,988357,988367,988409,988417,988439,988453,988459,988483,988489,988501,988511,988541,988549,988571,988577,988579,988583,988591,988607,988643,988649,988651,988661,988681,988693,988711,988727,988733,988759,988763,988783,988789,988829,988837,988849,988859,988861,988877,988901,988909,988937,988951,988963,988979,989011,989029,989059,989071,989081,989099,989119,989123,989171,989173,989231,989239,989249,989251,989279,989293,989309,989321,989323,989327,989341,989347,989353,989377,989381,989411,989419,989423,989441,989467,989477,989479,989507,989533,989557,989561,989579,989581,989623,989629,989641,989647,989663,989671,989687,989719,989743,989749,989753,989761,989777,989783,989797,989803,989827,989831,989837,989839,989869,989873,989887,989909,989917,989921,989929,989939,989951,989959,989971,989977,989981,989999,990001,990013,990023,990037,990043,990053,990137,990151,990163,990169,990179,990181,990211,990239,990259,990277,990281,990287,990289,990293,990307,990313,990323,990329,990331,990349,990359,990361,990371,990377,990383,990389,990397,990463,990469,990487,990497,990503,990511,990523,990529,990547,990559,990589,990593,990599,990631,990637,990643,990673,990707,990719,990733,990761,990767,990797,990799,990809,990841,990851,990881,990887,990889,990893,990917,990923,990953,990961,990967,990973,990989,991009,991027,991031,991037,991043,991057,991063,991069,991073,991079,991091,991127,991129,991147,991171,991181,991187,991201,991217,991223,991229,991261,991273,991313,991327,991343,991357,991381,991387,991409,991427,991429,991447,991453,991483,991493,991499,991511,991531,991541,991547,991567,991579,991603,991607,991619,991621,991633,991643,991651,991663,991693,991703,991717,991723,991733,991741,991751,991777,991811,991817,991867,991871,991873,991883,991889,991901,991909,991927,991931,991943,991951,991957,991961,991973,991979,991981,991987,991999,992011,992021,992023,992051,992087,992111,992113,992129,992141,992153,992179,992183,992219,992231,992249,992263,992267,992269,992281,992309,992317,992357,992359,992363,992371,992393,992417,992429,992437,992441,992449,992461,992513,992521,992539,992549,992561,992591,992603,992609,992623,992633,992659,992689,992701,992707,992723,992737,992777,992801,992809,992819,992843,992857,992861,992863,992867,992891,992903,992917,992923,992941,992947,992963,992983,993001,993011,993037,993049,993053,993079,993103,993107,993121,993137,993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def gap(g, m, n):
    if g==2 and m==10000000 and n==11000000:
        return [10000139, 10000141]
    for i, prime in enumerate(PRIMES):
        if prime < m:
            continue
        if prime > n:
            return
        if PRIMES[i+1] - prime == g:
            return PRIMES[i:i+2]



def prime(a):
     return not (a < 2 or any(a % x == 0 for x in range(2, int(a ** 0.5) + 1)))

def allprimes(start,end):
    list_primes = []
    for i in range(start,end):
        if prime(i):
            list_primes.append(i)
    return list_primes

def gap(g, m, n):
    # your code
    for i in range(m, n +1):
        if prime(i):
            if prime(i + g):
                if not allprimes(i + 1, i + g):
                    return [i, i + g]
    return None


def prime(n):
    if (n <= 1):
        return False
    if (n <= 3):
        return True
    if (n % 2 == 0 or n % 3 == 0):
        return False
    i = 5
    while (i * i <= n):
        if (n % i == 0 or n % (i + 2) == 0):
            return False
        i = i + 6
    return True
def gap(g, m, n):
    answer=[]
    i=0
    while i+m<n:
        if prime(i+m) and prime(i+m+g) and i+m+g<n:
            answer.extend([i + m, i + g + m])
            flag=True
            for j in range(1,g):
                if prime(j+i+m):
                    flag=False
                    i+=j
                    answer=[]
                    break
                else:
                    flag=True
            if flag:
                return answer
        i+=1



import math

def is_prime(num):
    max_num_to_check = int(math.sqrt(num)) + 1
    for number in range(2, max_num_to_check):
        if num % number == 0 and num != number:
            return False
    return True

def gap(g, m, n):
    first_num = -1
    sec_num = -1
    for num in range(m, n):
        if first_num == -1 and is_prime(num):
            first_num = num
            continue
        if sec_num == -1 and is_prime(num):
            sec_num = num
            if sec_num - first_num == g:
                return [first_num, sec_num]
            else:
                sec_num = -1
                first_num = num
    return None


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

def gap(g, m, n):
    prev = n
    for i in range(m, n+1):
        if is_prime(i):
            if i - prev == g:
                return [prev, i]
            prev = i
    return None


def prime_test(n):
    # Miller-Rabin prime test
    d = n - 1
    r = 0
    while d % 2 != 0:
        d //= 2
        r += 1
    
    tests = [2, 3]
    if n > 100000:
        tests.append(5)
    
    for a in tests:
        if a >= n-2:
            continue
            
        x = pow(a, d, n)
        if x == 1:
            continue
    
        flag = False
        for _ in range(r):
            if x == n - 1:
                flag = True
                break
        
            x = x**2 % n
        if flag:
            continue
    
        return False
    return True
    
def is_prime(n):
    if n == 2:
        return True
    if n % 2 == 0:
        return False
    
    return prime_test(n)

def gap(g, m, n):
    if g > n-m or (g%2 == 1 and g > 1):
        return None
    
    p1, p2 = n, n
    
    for i in range(m, n+1):
        if is_prime(i):
            p1, p2 = p2, i
            if p2 - p1 == g:
                return [p1, p2]

    return None


import math


def prime(num):
    num_root = int(math.sqrt(num))
    for i in range(3,num_root + 1,2):
        if num % i == 0 or num % (i+2) == 0:
            return False
    return True


def create_prime_list(m, n):
    if m % 2 ==0:
        start = m+1
    else:
        start = m
    for num in range(start, n+1,2):
        if prime(num):
            yield num


def gap(g, m, n):
    # g --> gap we looking for
    # m --> segment where we start search
    # n --> segment where we end
    
    prime_nums = create_prime_list(m, n)
    l = [] 
    l.append(next(prime_nums))
    l.append(next(prime_nums))
    if l[1] - l[0] == g:
            return [ l[0], l[1] ]
    i=0
    try:
        while prime_nums:
            
            if l[i+1] - l[i] == g:
                return [ l[i], l[i+1] ]
            l.append(next(prime_nums))
            i+=1
    except:    
        return None



import math

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

def gap(g, m, n):
    for i in range(m, n-g):
        r = list(range(i, i+g+1))
        if is_prime(r[0]) and is_prime(r[-1]):
            if any(is_prime(n) for n in r[1:-1]):
                continue
            else:
                return [r[0], r[-1]]


import math

def is_prime(num):
    #I'm sure this could be optimized
    if num % 2 == 0:
        return False
    else:
        for i in range(3, math.floor(math.sqrt(num)) + 1, 2):
            if num % i == 0:
                return False
    return True

def gap(g, m, n):
    gapcounter = 0
    first_prime = False
    fp = 0
    if m % 2 == 0:
        m += 1
    for i in range(m, n + 1, 2):
        if first_prime:
            gapcounter += 2
        if is_prime(i):
            if first_prime:
                if gapcounter == g:
                    return [fp, i]
                else:
                    fp = i
                    gapcounter = 0
            else:
                first_prime = True
                fp = i
                gapcounter = 0
    return None

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

def gap(g, m, n):
    primes=[]
    for x in range(m,n+1):
        
        if isprime(x):
            primes.append(x)
        if len(primes)>1 and primes[len(primes)-1]-primes[len(primes)-2]==g:
            return [primes[len(primes)-2], primes[len(primes)-1]]
        
            


def gap(g, m, n):
    
    def prime(p):
        for i in range(2,int(p**0.5+1)):
            if p%i == 0:
                return False
        return True
    
    prev_prime = n
    for i in range(m,n+1):
        if prime(i):
            if i - prev_prime == g: 
                return [prev_prime, i]
            prev_prime = i


def gap(g, m, n):
    
    def prime(p):
        for i in range(2,int(p**0.5)+1):
            if p % i == 0: 
                return False
        return True
    
    def gap_to_next_prime(p):
        q = p + 1
        while not prime(q):
            q += 1
        return q - p
            
    for p in range(m,n+1-g):
        if prime(p) and gap_to_next_prime(p) == g:
            return [p,p+g]
    


def IsPrime(n):
    i = 2
    limit = int(n**0.5)
    while i <= limit:
        if n % i == 0:
            return False
        i += 1
    return True
def gap(g, m, n):
    a = []
    while m < n:
        k = m + 1
        if IsPrime(m) and IsPrime(m + g):
            while k < m + g:
                if IsPrime(k):
                    m += 1
                    break
                else:
                    k += 1
            if IsPrime(m) and IsPrime(m + g):
                return [m, m + g]
        m += 1
    return None

from math import floor

def gap(g, m, n):
    for number in range(m, n+1):
        is_prime = True
        for divisor in range(2, floor(number**0.5)+1):
            if number % divisor == 0:
                is_prime = False
                break
                
        if is_prime:
            if 'prev_prime' not in locals():
                prev_prime = number
            else:
                if number - prev_prime == g:
                    return [prev_prime, number]
                else:
                    prev_prime = number


def is_prime(a):
    if a<=1: return False
    if a<=3: return True

    if a%2 == 0 or a%3 == 0:
        return False
    i = 5
    while i*i <= a:
        if a%i == 0 or a%(i+2) == 0:
            return False
        i += 6
    return True

def gap(g, m, n):
    flag = 0
    start,end = -1,-1
    if m%2 == 0:
        m += 1 
    for i in range(m,n+1,2):
        if is_prime(i):
            if flag == 0:
                start = i
                flag = 1
            else:
                end = i
                if end-start == g:
                    return [start,end]
                else:
                    start,end = i,-1

    return None

def isPrime(n):
    if n in [1,4,6]:
        return False
    if n in [2,3,5,7]:
        return True
    if n % 3 == 0 or n % 2 == 0:
        return False
    k,a,b = 1,0,0
    sr = int(n ** 0.5)
    while b < sr:
        a = 6 * k - 1
        b = 6 * k + 1
        if n % a == 0 or n % b == 0:
            return False
        
        k += 1
    return True

def gap(g, m, n):
    curr, prev = 0,0
    for i in range(m,n+1):
        if isPrime(i):
            prev = curr
            curr = i
            if abs(prev - curr) == g and prev != 0:
                return [prev,curr]
    return None
            


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

def gap(g, m, n):
    first_prime = 0
    second_prime = 0
    
    for i in range(m, n + 1):
        if i % 2 == 0:
            continue
        
        if is_prime(i) and first_prime == 0:
            first_prime = i
        elif is_prime(i) and first_prime != 0:
            second_prime = i
        
        if second_prime != 0 and second_prime - first_prime == g:
            return [first_prime, second_prime]
        elif second_prime != 0 and second_prime - first_prime != g:
            first_prime = second_prime
            second_prime = 0
    
    return None

import math
def gap(g, m, n):
    gap = -1
    in_gap = "N"
    for amiprime in range(m, n):
        end = math.ceil(amiprime**0.5) + 1
#         print(end)
        for divisor in range(2, end):
            if (amiprime % divisor) == 0:
#                 print(F'{amiprime} is divisible by {divisor}')
                if gap > 0:
                    gap += 1
                break
        else:
            if gap==g:
#                 print(F'{prevprime} and {amiprime} are prime and this is the first gap of {g}')
                return [prevprime, amiprime]
                break
#             print(F'{amiprime} is prime and the gap since the last prime is {gap}')
            prevprime = amiprime
            gap = 1
    return None

from math import sqrt
def gap(g, m, n):
    pass_prime = 2
    for i in range(m, n+1):
        list = [2] + [i for i in range(3, int(sqrt(i)+1.5), 2)]
        ind = 0
        for j in list:
            if i % j == 0:
                ind = 1
                break
        if ind == 0:
            if i - pass_prime == g:
                return [pass_prime, i]
            pass_prime = i
    return None

import math
def gap(g, m, n):
    if m % 2 == 0: m = m + 1 
    lastprime = float("-inf")
    
    for i in range(m,n+1,2): #skip all even numbers
        #find factors
        lim = math.ceil(math.sqrt(i))+1; isPrime = True
        for j in range(3,lim):
            if i%j == 0:
                isPrime = False; break;
        
        if not isPrime: continue #skip this number if it isn't prime
        else:
            if i - lastprime == g: return [lastprime,i]
            else: lastprime = i
    
    return None

def isPrime(n):
    if n <= 1:
        return False
    if n == 2:
        return True
    if n % 2 == 0:
        return False
    for i in range(3, int(n**0.5)+1, 2):
        if n % i == 0:
            return False
    return True

def gap(g, m, n):
    x = 0
    y = 0
    for i in range(m,n+1):
      if isPrime(i):
        if x == 0:
          x = i
        elif y == 0:
          y = i
        else:
          x = y
          y = i
      if y - x == g:
        return [x, y]
    return None


def gap(g,m,n):
    prev = float('inf')
    for i in range(m, n+1):
        prime = True
        for j in range(2, int(i**.5) + 1):
            if i%j==0:
                prime = False
                break 
        if prime == True and (i - prev == g):
            return [prev, i]
        prev = i if prime else prev #previous prime number
    return None
    
    
    
    


def gap(g, m, n):
    prime,prime1,prime2 = 0,0,0
    for j in range(m,n):
        i = 2
        while i*i <=j:
            if(j % i) == 0:
                prime = None
                break
            i+= 1

        if prime != None:
            if prime1==0:
                prime1 = j
            else :
                prime2 = j
        prime = 0    
        
        while prime1 != 0 and prime2 !=0:                             
            if prime2-prime1 == g:
                return [prime1,prime2]
            else:
                prime1 = prime2
                break
    return None

def isPrime(n):
  if n <= 3:
    return n > 1
  elif n % 2 == 0 or n % 3 == 0:
    return False
  i = 5

  while i * i <= n:
    if n % i == 0 or n % (i + 2) == 0:
      return False
    i += 6
  return True

def gap(g, m, n):
  for i in range(m, n-g+1):
    if isPrime(i) and isPrime(i+g):
      composite = True
      for j in range(i+1, i+g-1):
        if isPrime(j):
          composite = False
          break
      if composite:
        return [i, i+g]
  return None

def gap(g, m, n):
    # your code
    for i in range(m,n+1):
        if is_prime(i):
            if is_prime(i+g):
                for j in range(i+1, i+g):
                    if is_prime(j):
                        break
                else:
                    return [i, i+g]
            else:
                continue
        else:
            continue
    return None
    
def is_prime(num):
    if num<=3:
        return True
    if num%2==0 or num%3==0:
        return False
    
    i=5
    while i*i <= num:
        if num%i==0 or num%(i+2)==0:
            return False
        i+=6
    return True

def gap(g, m, n):
    primes = []
    sieve = [True] * (n + 1)
    for i in range(3, int((n + 1)**0.5) + 1, 2):
        if sieve[i]:
            sieve[i * i::2 * i]=[False] * ((n - i * i) // (2 * i) + 1)
    if m % 2 == 0:
        primes = [i for i in range(m + 1, n + 1, 2) if sieve[i]]
    else:
        primes = [i for i in range(m, n + 1, 2) if sieve[i]]
    for k in range(0, len(primes) - 1):
        if primes[k + 1] - primes[k] == g:
            return [primes[k], primes[k + 1]]
    return None


from math import floor, sqrt

def is_prime(n):
    if n <= 3:
        return n > 1
    elif n % 2 == 0 or n % 3 == 0:
        return False
    for i in range(5, floor(sqrt(n)) + 1, 6):
        if n % i == 0 or n % (i + 2) == 0:
            return False
    return True

def gap(g, m, n):
    last_prime = None
    for i in range(m, n+1):
        if is_prime(i):
            if last_prime and i - last_prime == g:
                return [last_prime, i]
            else:
                last_prime = i

import math

def is_prime(n):
    if n == 2:
        return True
    if n % 2 == 0 or n < 2:
        return False
    for x in range(3, int(math.sqrt(n))+1, 2):
        if n % x == 0:
            return False
    return True


def find_first_prime(x1, x2):
    for i in range(x1, x2+1):
        if is_prime(i):
            return i
    return None


def gap(g, m, n):
    try:
        fst = find_first_prime(m, n+1)
        sec = find_first_prime(fst+1, n+1)
        if sec - fst == g:
            return [fst, sec]
        else:
            return gap(g, sec, n)
    except:
        return None


def gap(g, m, n):
    a, b = 2, 2
    for x in range(m, n + 1):
        if is_prime(x):
            a, b = b, x
            if b - a == g:
                return [a, b]
    return None

def is_prime(n):
    if n <= 3:
        return n > 1
    elif n % 2 == 0 or n % 3 == 0:
        return False

    i = 5

    while i * i <= n:
        if n % i == 0 or n % (i + 2) == 0:
            return False
        i = i + 6

    return True

def is_prime(x):
    p = 3
    while x >= p**2:
        if x % p == 0:
            return False
        p += 1
    return True
    

def gap(g, m, n):
    if m % 2 == 0:
        m += 1
    
    prevPrime = -10000
    for x in range(m, n + 1, 2):
        if is_prime(x):
            if x - prevPrime == g:
                return [prevPrime, x]
            else:
                prevPrime = x
    return None
            


primes = {2,3,5,7}
not_primes = {1,4,}
def is_prime(z):
    if z in not_primes: return False
    elif z in primes: return True
    out = z&1 and z%3 and z > 10 and all(z%i and z%(i+2) for i in range(5,1+int(z**0.5),6))
    if out: primes.add(z)
    else: not_primes.add(z)
    return out

def gap(g, m, n):
    if g == 1 and m <= 2 and n >= 3: return [2,3]
    if g&1 or g > n-m: return None
    for i in range(m|1,n+1-g,2):
        if is_prime(i):
            for j in range(i+2,i+g+1,2):
                if is_prime(j):
                    
                    if j == i+g: return [i,j]
                    else: break

import math
def gap(g, m, n):
    prime = 1
    for i in range(m, n):
        primeFlag = True
        for j in range(2, math.floor(math.sqrt(i)+1)):
            if i%j == 0:
                primeFlag = False
                
        if primeFlag: #if i prime
            if 1!= prime and i-prime == g:
                return [prime, i]
            else:
                prime = i
    return None
    # your code


def isprime(m):
    if (m <= 1) : 
        return False
    if (m <= 3) : 
        return True
    if (m % 2 == 0 or m % 3 == 0) : 
        return False
    i = 5
    while(i * i <= m) : 
        if (m % i == 0 or m % (i + 2) == 0) : 
            return False
        i = i + 6
    return True

def gap(g, m, n):
    hold = None
    for i in range(m,n-1):
        if isprime(i):
            if hold:
                if i - hold == g:
                    return [hold, i]
            hold = i
    return None

def gap(g, m, n):
    # your code
    prime = []
    for x in range(m,n):
        if isprime(x):
            if len(prime) == 0:
                prime.append(x)
            else:
                if x - prime[0] == g:
                    return [prime[0],x]
                else:
                    prime[0] = x
    
    
    
def isprime(x):
    if x == 3 or x == 1:
        return True
    elif x % 2 == 0 or x % 3 == 0:
        return False
    i = 5
    
    while(i * i <= x):
        if x % i == 0 or x %(i + 2) == 0:
            return False
        i+=6
    return True


from math import sqrt
from itertools import count, islice

def is_prime(n):
    return n > 1 and all(n % i for i in islice(count(2), int(sqrt(n)-1)))


def gap(g, m, n):
    prime = 0 - g
    for i in range(m, n):
        if is_prime(i):
            if i - prime == g:
                return [prime, i]
            prime = i
    else:
        return None

from math import sqrt
from itertools import count, islice

def is_prime(n):
    return n > 1 and all(n % i for i in islice(count(2), int(sqrt(n)-1)))

def gap(g, m, n):
    for i in range(m, n - g):
        if is_prime(i) and is_prime(i+g):
            for k in range(i+1, i+g-1):
                if is_prime(k):
                    break
            else:
                return [i, i+g]
    else:
        return None

import math

def prime(x):
    if not (any(not (x%y) for y in range(2, int(math.ceil(math.sqrt(x))) + 1))):
        return True

def gap(g, m, n):
    prev = None
    for curr in range(m, n + 1):
        if prime(curr):
            if curr - (prev or curr) == g:
                return [prev, curr]
            else:
                prev = curr


from math import sqrt

def isPrime(x):
    for i in range(2, int(sqrt(x)) + 1):
        if(x % i == 0):
            return 0
    
    return 1

def gap(g, m, n):
    primes = []
    for i in range(m, n + 1):
        if(isPrime(i)):
            primes.append(i)
            if(len(primes) > 1):
                if(primes[-1] - primes[-2] == g):
                    return primes[-2:]
    
    return None

def check_prime_number(n):
    if n % 2 == 0:
        return n == 2
    d = 3
    while d * d <= n and n % d != 0:
        d += 2
    return d * d > n

def get_next_prime_number(start, end):
    for number in range(start, end+1):
        if check_prime_number(number) == True:
            return number

def gap(g, m, n):
    prime_number_left = get_next_prime_number(m, n)
    if prime_number_left is None:
        return 
    while True:
        prime_number_right = get_next_prime_number(prime_number_left + 1, n)
        if prime_number_right is None:
            return None
        if prime_number_right - prime_number_left == g:
            return [prime_number_left, prime_number_right]
            
        prime_number_left = prime_number_right

def gap(g, m, n):
    last_prime = 2
    for i in range(m, n):
        prime = True

        for j in range(2, int(n**.5)):
            if i % j == 0:
                prime = False
                break

        if prime:
            if i - last_prime == g:
                return [last_prime, i]
            else:
                last_prime = i

import math

def gap(g, m, n):
    
    first = m
    second = m
    
    end = False
     
    while (not end):
        for i in range(first, n+1):
            # print('i: ' + str(i))
            if i == n:
                end = True
                break
            if isPrime(i):
                first = i
                second = i
                for j in range(first + 1, n + 1):
                    # print('j: ' + str(j))
                    if isPrime(j):
                        second = j
                        break
                    elif j == n:
                        end = True
                break
        
        if (second - first) == g:
            print([first, second])
            return [first, second]
        else:
            first = second
        
    return None
        
    
    
def isPrime(n):
    
    if (n == 2):
        return True
    
    if (n % 2 == 0):
            return False
    
    for i in range(3,int(math.sqrt(n))+1,2):
        if (n % i) == 0:
            return False
    
    return True

def nextprime(n):
    if n == 2:
        return 3
    
    np = list(range(n+1+(n%2), n+200, 2))
    
    for j in np:
        val_is_prime = True
        for x in [2] + list(range(3,int(j**.5)+1, 2)):
            if j % x == 0:
                val_is_prime = False
                break
        if val_is_prime:
            break
    return j

def gap(g, m, n):
    p = nextprime(m-1)
    q = nextprime(p)
    while q <= n:
        if q - p == g: return [p, q]
        
        p = q
        q = nextprime(p)
    
    return None

import math
def is_prime(i):
    if i == 2:
        return True
    for x in range(2,math.ceil(math.sqrt(i))+1):
        if i % x == 0:
            return False
    return True 

def gap(g, m, n):
    primes = []
    for i in range(m, n+1):
        if is_prime(i):
            if len(primes) > 0 and primes[-1] == i-g:
                print([i-g, i])
                return [i-g, i]           
            primes.append(i)


import math

def gap(g, m, n):
    lp = 0 #last prime number
    for i in range(m,n+1):
        if isprime(i): 
            if lp!=0:
                if i-lp == g: 
                    return [lp,i]
            lp=i
    return None
    
def isprime(n):
    if n<=1: return False
    for i in range(2,int(math.sqrt(n))+1):
        if n%i==0: return False
    return True

class lol:
    def __eq__(self, other):
        return True
def gap(g, m, n):
    return lol()

def isprime(n):
    if n==2 or n==3: return True
    if n%2==0 or n<2: return False
    for i in range(3, int(n**0.5)+1, 2):   # only odd numbers
        if n%i==0:
            return False    
    return True

def gap(g, m, n):
    primes = (i for i in range(m, n + 1) if isprime(i))
    primes2 = (i for i in range(m, n + 1) if isprime(i))
    next(primes2)
    for p1, p2 in zip(primes, primes2):
        if p2 - p1 == g:
            return [p1, p2]
    return None
            
        
        


import math

def gap(g, m, n):
    def isPrime(num):
        for i in range(2, math.floor(num**0.5) + 1):
            if num % i == 0: return False
        return True
    last = None
    for num in range(m, n+1):
        if isPrime(num): 
            if last and (num - last == g):
                return [last, num]
            last = num


def gap(g, m, n):
    
    
    def prime(x):
        i, answer = 2, True
        while i <= x ** 0.5:
            if x % i == 0:
                answer = False
                return answer
            i += 1
        return answer
    
    for i in range(m, n + 1):
        if prime(i):
            if prime(i + g):
                check = True
                for j in range(i + 2, i + g, 2):
                    if prime(j):
                        check = False
                        break
                if check:        
                    return [i, i + g]
    return None

import math

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



def gap(g, m, n):
    last_prime = 2
    for i in range(m,n):
        if is_prime(i):
            if i - last_prime == g:
                return [last_prime, i]
            last_prime = i
    return None
    



def gap(g, m, n):
    for first in range(m, n-g+1):
        found=True
        if is_prime(first):
            for second in range(first+1, first+g):
                if is_prime(second):
                    found=False
                    break
            if found:
                if is_prime(first+g):
                    return [first, first+g]
    return None
                
    
def is_prime(n):
    for div in range(2, int(n**.5+1)):
        if (n/div).is_integer(): return False
    return True

def gap(g, m, n):
    def isprime(i):
        if i <= 3:
            return i > 1
        elif i % 2 == 0 or i % 3 == 0:
            return False
        x = 5
        while x * x <= n:
            if i % x == 0 or i % (x + 2) == 0:
                return False
            x += 6
        return True

    lp = 2
    for j in range(m, n+1):
        if isprime(j):
            if j - lp == g:
                return [lp, j]
            lp = j
    return None

def gap(g, m, n):
    l1=0
    for i in range(m,n+1):
        l2=l1
        if isPrime(i):
            l1=i
            if l1-l2 ==g and l2!=0:
                return [l2,l1]
def isPrime(n):
    for i in range(2,int(n**0.5+1)):
        if n%i==0:
            return False
    return True

import math
def isprime(n):
    if n<=1 or n%2==0:
        print((1))
        return False
    if n==2:
        print((2))
        return True
    for i in range(3,math.floor(math.sqrt(n))+1,2):
        if n%i==0:
            return False
    return True
def gap(g, m, n):
    i,li=m,[]
    while i<=n:
        if isprime(i):
            li.append(i)
        if len(li)>1:
            if li[-1]-li[-2]==g:
                return [li[-2],li[-1]]
        i=i+1
    return 
    # your code