






import math






def 						a    (		lowerCamelCase_       ):






    '''simple docstring'''

    if 1 < number < 4:
        # 2 and 3 are primes
        return True
    elif number < 2 or number % 2 == 0 or number % 3 == 0:
        # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
        return False

    # All primes number are in format of 6k +/- 1
    for i in range(5	,     int(math.sqrt(lowerCamelCase_       ) + 1       )	,     6       ):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True






def 						a    (		lowerCamelCase_ = 0.1       ):






    '''simple docstring'''
    lowercase__     				=    3
    lowercase__     				=    3

    while primes / (2 * j - 1) >= ratio:
        for i in range(j * j + j + 1	,     (j + 2) * (j + 2)	,     j + 1       ):
            primes += is_prime(lowerCamelCase_       )
        j += 2
    return j


if __name__ == "__main__":
       import doctest

       doctest.testmod()












def 						a    (		lowerCamelCase_	,     lowerCamelCase_	,     lowerCamelCase_       ):






				'''simple docstring'''

				if exponent == 1:
								return base
				if exponent % 2 == 0:
								lowercase__     				=    _modexpt(lowerCamelCase_	,     exponent // 2	,     lowerCamelCase_       ) % modulo_value
								return (x * x) % modulo_value
				else:
								return (base * _modexpt(lowerCamelCase_	,     exponent - 1	,     lowerCamelCase_       )) % modulo_value






def 						a    (		lowerCamelCase_ = 1777	,     lowerCamelCase_ = 1855	,     lowerCamelCase_ = 8       ):






				'''simple docstring'''
				lowercase__     				=    base
				for _ in range(1	,     lowerCamelCase_       ):
								lowercase__     				=    _modexpt(lowerCamelCase_	,     lowerCamelCase_	,     10**digits       )

				return result


if __name__ == "__main__":
							print(F"{solution() = }")




