# Definition (Primorial Of a Number)

*Is similar to factorial of a number*, **_In primorial_**, not all the natural numbers get multiplied, **_only prime numbers are multiplied to calculate the primorial of a number_**. It's denoted with **_P_****_#_** and it is the product of the first n prime numbers.
___ 

# Task

**_Given_** *a number N* , **_calculate its primorial_**. ![!alt](https://i.imgur.com/mdX8dJP.png)  ![!alt](https://i.imgur.com/mdX8dJP.png)  
___

# Notes

* **_Only positive_** numbers *will be passed (N > 0)* .
___

# Input >> Output Examples:

``` cpp
1- numPrimorial (3) ==> return (30)
```

## **_Explanation_**:

**_Since_** *the passed number is (3)* ,**_Then_** **_the primorial_** *should obtained by multiplying*  ```2 * 3 * 5 = 30 .```

### Mathematically written as , **_P_**3**_#_** = 30 .
___ 

## **_Explanation_**:

**_Since_** *the passed number is (5)* ,**_Then_** **_the primorial_** *should obtained by multiplying*  ``` 2 * 3 * 5 * 7 * 11 = 2310 .```

### Mathematically written as , **_P_**5**_#_** = 2310 .
___

## **_Explanation_**: 

**_Since_** *the passed number is (6)* ,**_Then_** **_the primorial_** *should obtained by multiplying*  ``` 2 * 3 * 5 * 7 * 11 * 13 = 30030 .```

### Mathematically written as , **_P_**6**_#_** = 30030 .
___
___
___

# [Playing with Numbers Series](https://www.codewars.com/collections/playing-with-numbers)

# [Playing With Lists/Arrays Series](https://www.codewars.com/collections/playing-with-lists-slash-arrays)

# [For More Enjoyable Katas](http://www.codewars.com/users/MrZizoScream/authored)
___

## ALL translations are welcomed

## Enjoy Learning !!
# Zizou

Difficulty: introductory

Starter code:

def num_primorial(n):
	

Solutions:
def num_primorial(n):
    primorial, x, n = 2, 3, n-1
    while n:
        if all(x % d for d in range(3, int(x ** .5) + 1, 2)):
            primorial *= x
            n -= 1
        x += 2
    return primorial

def num_primorial(n):
    primNums = [
     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,
    ]
    prod = 1
    for i in range(n):
        prod *= primNums[i]
    return prod

def num_primorial(n):
    p = []
    val = 2
    while len(p)<n:
        for div in p:
            if val%div==0:
                val += 1
                break
        else:
            p.append(val)
    val = 1
    for x in p:
        val *= x
    return val


def num_primorial(n):
    """
    Custom Sieve method used...
    """
    prime_list = [2]
    ans = prime_list[0]
    chk_num = 3
    while len(prime_list) != n:
        for prime in prime_list:
            if chk_num % prime == 0:
               break
            elif prime == prime_list[-1]: # and chk_num%prime != 0
                prime_list.append(chk_num)   # chk_num is prime
                ans = ans*prime_list[-1] # update answer
        chk_num = chk_num + 2 #all primes after 2 are odd
    return ans



def isprime(x): #function to check if number is a prime number
    number = x
    if number==2:
        return(True)
    else:
        for num in range(2,number):
            if number%num ==0:
                return(False)
        else:
            return(True)

def num_primorial(num_of_nums):
    counter = 0 # counter to keep track of how many numbers prime numbers we've multipled
    number = 2 #arbitray number to start keeping track of prime numbers
    primorial=1 #return variable which we will multiple all discovered prime numbers by until counter == num_of_nums

    
    for x in range(2,10000):
        if isprime(number) == True: 
            primorial *=x
            number+=1#keep our number counter going up to test for more prime numbers
            counter+=1
            if counter == num_of_nums:# to break the loop once we have the desired amount of prime numbers multipled
                break
        else:
            number+=1 #keep our number counter going up to test for more prime numbers
    return(primorial)
            


import math as mt   
MAX=10000  
prime=[True for i in range(MAX+1)] 
def Sieve():      
    prime[1]=False
      
    for p in range(2,mt.ceil(mt.sqrt(MAX))):   
        if prime[p]: 
           
            for i in range(2*p,MAX+1,p): 
                prime[i]=False
Sieve()                  
def num_primorial(n):
    count,num=0,1     
    prod=1
    while count<n:
          
        if prime[num]: 
            prod*=num 
            count+=1
        num+=1
    return prod 

def num_primorial(n):
    l = [2]
    k = 3
    while len(l) < n:
        l.append(k)
        for i in range(2, k):
            if k % i == 0:
                l.pop()
                break
        k += 1
    out = 1
    for i in l:
        out *= i
    return out

from functools import reduce


def primes_sieve(n):
    sieve = [False, False] + [True] * (n - 1)
    limit = int(n ** 0.5) + 1
    for k in range(2, limit):
        if sieve[k]:
            i = k * 2
            l = (n - k) // k
            sieve[i::k] = [False] * l
    return [p for p, is_prime in enumerate(sieve) if is_prime]


primes = primes_sieve(8000)


def num_primorial(n):
    return reduce(int.__mul__, primes[:n])

from itertools import accumulate, count
from collections import defaultdict
from operator import mul

def gen():
    D = defaultdict(list)
    for q in count(2):
        if q not in D:
            yield q
            D[q*q] = [q]
        else:
            for p in D[q]: D[p+q].append(p)
            del D[q]
create, save = accumulate(gen(), mul), [1]

def num_primorial(n):
    while len(save) <= n: save.append(next(create))
    return save[n]

def num_primorial(n):
    def isprime(p):
        return p > 1 and all(p % i > 0 for i in range(2,int(p**.5+1)))
    primorial,p,c = 1,1,0
    while c < n:
        if isprime(p):
            primorial *= p
            c += 1
        p += 1
    return primorial

import math
def isPrime(n):
    for i in range(2,int(math.sqrt(n))+1):
        if n%i==0:
            return False
    return True
def num_primorial(n):
    s,j=1,0
    for i in range(2,n**2):
        if isPrime(i):
            s*=i
            j+=1
            if j==n:
                return s

from functools import reduce
def num_primorial(n):
    from operator import mul
    from functools import reduce
    lst = []
    i = 2
    while (len(lst)!=n):
        for j in range(2,i):
            if i%j == 0:
                break
        else:
                lst.append(i)
        i+=1
    return reduce(mul,lst)


def num_primorial(n):
    prim = 2
    x = 3
    while n - 1:
        if all(x % num != 0 for num in range(3, int(x ** 0.5) + 1, 2)):
            prim *= x
            n -= 1
        x += 2
    return prim

def num_primorial(n):
    i = 2
    sum = 1
    k = 0
    while True:
        for j in range(2, i):
            if i % j == 0:
                break
        else:
            sum *= i
            k += 1
        if k == n:
            break
        i += 1
    return sum 

def is_prime(a):
    if a < 4:
        return True
    for i in range(2,int(a/2)+1):
        if a%i == 0:
            return False
    return True

def num_primorial(n):
    result = 1
    count_primes = 0
    i = 2
    while count_primes < n:
        if is_prime(i):
            result *= i
            count_primes += 1
        i += 1
    return result

def num_primorial(n):
    lst=[2]
    for i in range(2,7919):
        count=0
        for e in lst:
            if i%e==0:
                count=count+1
        if count==0:
            lst.append(i)
        if len(lst)==n:
            break

    prod=1
    for e in range(n):
        prod=prod*lst[e]
    return prod  


def num_primorial(n):
    primes = [2]
    i = 1
    new_p = 2
    while i < n:
        j = 0
        while j < len(primes):
            if new_p % primes[j] == 0:
                new_p += 1
                break
            else: j += 1
        if j == len(primes): 
            primes = primes + [new_p]
            new_p += 1
            i += 1
    product = primes[0]
    for p in primes[1:]: product *= p
    return product
        


import math
from functools import reduce
#finding primes
MAX_PRIME = 10000
prime_candidates = [True] * MAX_PRIME

for i in range (2,int(math.sqrt(MAX_PRIME)) + 1):
    if prime_candidates[i] == True:
        for j in range(i**2, MAX_PRIME, i):
            prime_candidates[j] = False


def num_primorial(n):
    primes = [i for i,j in enumerate(prime_candidates) if j == True][2:]
    return reduce(lambda x,y : x*y, primes[0:n])

from functools import reduce
from operator import mul

PRIMES = [2] + [x for x in range(3, 10**4, 2) if all(x%d for d in range(3, int(x**0.5)+1, 2))]

def num_primorial(n):
    return reduce(mul, PRIMES[:n])