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

Source: codewars | Difficulty: EASY
Tags: Fundamentals

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 ** 0.5 + 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 ** 0.5) + 1, 2))):
			if x - prev == g:
				return [prev, x]
			prev = x


import numpy as np
sieve = np.ones(12000000, 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):
			if isprime(i + g):
				if not any(list([isprime(x) for x in list(range(i + 1, i + g))])):
					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 ** 0.5) + 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


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
	while True:
		if current_number > n:
			return None
		if prime_test(current_number) == 'not_prime':
			current_number = current_number + 1
		elif prime_test(current_number + g) == 'not_prime':
			current_number = current_number + 1
		else:
			prime_in_between = 0
			for i in range(current_number + 2, current_number + g):
				if prime_test(i) == 'prime':
					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
				elif 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 ** 0.5) + 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


def isPrime(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(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


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):
		if not is_prime(t):
			continue
		if first == 0:
			first = t
		elif t - first == g:
			return [first, t]
		else:
			first = t
	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 ** 0.5) + 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, 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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, 993169, 993197, 993199, 993203, 993211, 993217, 993233, 993241, 993247, 993253, 993269, 993283, 993287, 993319, 993323, 993341, 993367, 993397, 993401, 993407, 993431, 993437, 993451, 993467, 993479, 993481, 993493, 993527, 993541, 993557, 993589, 993611, 993617, 993647, 993679, 993683, 993689, 993703, 993763, 993779, 993781, 993793, 993821, 993823, 993827, 993841, 993851, 993869, 993887, 993893, 993907, 993913, 993919, 993943, 993961, 993977, 993983, 993997, 994013, 994027, 994039, 994051, 994067, 994069, 994073, 994087, 994093, 994141, 994163, 994181, 994183, 994193, 994199, 994229, 994237, 994241, 994247, 994249, 994271, 994297, 994303, 994307, 994309, 994319, 994321, 994337, 994339, 994363, 994369, 994391, 994393, 994417, 994447, 994453, 994457, 994471, 994489, 994501, 994549, 994559, 994561, 994571, 994579, 994583, 994603, 994621, 994657, 994663, 994667, 994691, 994699, 994709, 994711, 994717, 994723, 994751, 994769, 994793, 994811, 994813, 994817, 994831, 994837, 994853, 994867, 994871, 994879, 994901, 994907, 994913, 994927, 994933, 994949, 994963, 994991, 994997, 995009, 995023, 995051, 995053, 995081, 995117, 995119, 995147, 995167, 995173, 995219, 995227, 995237, 995243, 995273, 995303, 995327, 995329, 995339, 995341, 995347, 995363, 995369, 995377, 995381, 995387, 995399, 995431, 995443, 995447, 995461, 995471, 995513, 995531, 995539, 995549, 995551, 995567, 995573, 995587, 995591, 995593, 995611, 995623, 995641, 995651, 995663, 995669, 995677, 995699, 995713, 995719, 995737, 995747, 995783, 995791, 995801, 995833, 995881, 995887, 995903, 995909, 995927, 995941, 995957, 995959, 995983, 995987, 995989, 996001, 996011, 996019, 996049, 996067, 996103, 996109, 996119, 996143, 996157, 996161, 996167, 996169, 996173, 996187, 996197, 996209, 996211, 996253, 996257, 996263, 996271, 996293, 996301, 996311, 996323, 996329, 996361, 996367, 996403, 996407, 996409, 996431, 996461, 996487, 996511, 996529, 996539, 996551, 996563, 996571, 996599, 996601, 996617, 996629, 996631, 996637, 996647, 996649, 996689, 996703, 996739, 996763, 996781, 996803, 996811, 996841, 996847, 996857, 996859, 996871, 996881, 996883, 996887, 996899, 996953, 996967, 996973, 996979, 997001, 997013, 997019, 997021, 997037, 997043, 997057, 997069, 997081, 997091, 997097, 997099, 997103, 997109, 997111, 997121, 997123, 997141, 997147, 997151, 997153, 997163, 997201, 997207, 997219, 997247, 997259, 997267, 997273, 997279, 997307, 997309, 997319, 997327, 997333, 997343, 997357, 997369, 997379, 997391, 997427, 997433, 997439, 997453, 997463, 997511, 997541, 997547, 997553, 997573, 997583, 997589, 997597, 997609, 997627, 997637, 997649, 997651, 997663, 997681, 997693, 997699, 997727, 997739, 997741, 997751, 997769, 997783, 997793, 997807, 997811, 997813, 997877, 997879, 997889, 997891, 997897, 997933, 997949, 997961, 997963, 997973, 997991, 998009, 998017, 998027, 998029, 998069, 998071, 998077, 998083, 998111, 998117, 998147, 998161, 998167, 998197, 998201, 998213, 998219, 998237, 998243, 998273, 998281, 998287, 998311, 998329, 998353, 998377, 998381, 998399, 998411, 998419, 998423, 998429, 998443, 998471, 998497, 998513, 998527, 998537, 998539, 998551, 998561, 998617, 998623, 998629, 998633, 998651, 998653, 998681, 998687, 998689, 998717, 998737, 998743, 998749, 998759, 998779, 998813, 998819, 998831, 998839, 998843, 998857, 998861, 998897, 998909, 998917, 998927, 998941, 998947, 998951, 998957, 998969, 998983, 998989, 999007, 999023, 999029, 999043, 999049, 999067, 999083, 999091, 999101, 999133, 999149, 999169, 999181, 999199, 999217, 999221, 999233, 999239, 999269, 999287, 999307, 999329, 999331, 999359, 999371, 999377, 999389, 999431, 999433, 999437, 999451, 999491, 999499, 999521, 999529, 999541, 999553, 999563, 999599, 999611, 999613, 999623, 999631, 999653, 999667, 999671, 999683, 999721, 999727, 999749, 999763, 999769, 999773, 999809, 999853, 999863, 999883, 999907, 999917, 999931, 999953, 999959, 999961, 999979, 999983]

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):
	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 prime_test(n):
	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):
	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):
	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
			elif 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
		for divisor in range(2, end):
			if amiprime % divisor == 0:
				if gap > 0:
					gap += 1
				break
		else:
			if gap == g:
				return [prevprime, amiprime]
				break
			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):
		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
		elif 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 ** 0.5) + 1):
			if i % j == 0:
				prime = False
				break
		if prime == True and i - prev == g:
			return [prev, i]
		prev = i if prime else prev
	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):
	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 1 != prime and i - prime == g:
				return [prime, i]
			else:
				prime = i
	return None


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):
	prime = []
	for x in range(m, n):
		if isprime(x):
			if len(prime) == 0:
				prime.append(x)
			elif 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):
	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 ** 0.5)):
			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):
			if i == n:
				end = True
				break
			if isPrime(i):
				first = i
				second = i
				for j in range(first + 1, n + 1):
					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 ** 0.5) + 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
	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):
		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 ** 0.5 + 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