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Is there a way to list super primes (primes in a prime position wikipedia article) between 1 and n using NumPy.

Gabe
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  • @msanford --the question is about generating "super primes" not regular primes. – DarrylG Dec 29 '21 at 16:05
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    Why `numpy`? Is it something that can be calculated from a array like `arange(1,n)` with whole_array operations? Or is the task inherently iterative, evaluating each number in sequence? – hpaulj Dec 29 '21 at 16:42
  • True @DarrylG; that notwithstanding this is _not remotely_ an on-topic question for SO. I voted to close as a duplicate in an attempt to be mildly helpful in the process. – msanford Dec 29 '21 at 19:04
  • Does this answer your question? [Simple prime number generator in Python](https://stackoverflow.com/questions/567222/simple-prime-number-generator-in-python) – President James K. Polk Dec 29 '21 at 23:54
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    Are we no longer expecting questioners to demonstrate even the slightest attempt at solving their own problems anymore? – President James K. Polk Dec 29 '21 at 23:56

2 Answers2

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I got this without Numpy, is that okay? here is the code based on

Sieve of Atkin

import math

is_prime = list()
limit = 100
for i in range(5, limit):
    is_prime.append(False)

for x in range(1, int(math.sqrt(limit)) + 1):
    for y in range(1, int(math.sqrt(limit)) + 1):
        n = 4 * x ** 2 + y ** 2
        if n <= limit and (n % 12 == 1 or n % 12 == 5) and n <= len(is_prime):
            # print "1st if"
            is_prime[n] = not is_prime[n]
        n = 3 * x ** 2 + y ** 2
        if n <= limit and n % 12 == 7:
            # print "Second if"
            is_prime[n] = not is_prime[n]
        n = 3 * x ** 2 - y ** 2
        if x > y and n <= limit and n % 12 == 11:
            # print "third if"
            is_prime[n] = not is_prime[n]

for n in range(5, int(math.sqrt(limit))):
    if is_prime[n]:
        for k in range(n ** 2, limit + 1, n ** 2):
            if k <= len(is_prime):
                is_prime[k] = False
for n in range(5, limit):
    if n < len(is_prime) and is_prime[n]:
        print(n)
Feras Alfrih
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0

Numpy Code Version

Sieve modification of Numpy Sieve by user2357112 supports Monica

import numpy as np

def sieve(n):
    '''
        Sieve of Erastosenes using numpy
    '''
    flags = np.ones(n, dtype=bool)  # Set all values to True
    
    # Set 0, 1, and even numbers > 2 to False
    flags[0] = flags[1] = False
    flags[4:n:2] = False  
    for i in range(3, n, 2):
        # Check for odd primes
        if flags[i]:
            flags[i*i::i] = False
            
    return np.flatnonzero(flags)    # Indexes of True are prime

def superPrimes(n):
    '''
        Find superprimes
    '''
    # Find primes up to n using sieve
    p = sieve(n)

    # p(i) denotes the ith prime number, the numbers in this sequence are those of the form p(p(i))
    # Want to find numbers we can index in the list (i.e. has to be less than len(p))
    indexes = p[p < len(p)]             # base 1 indexes within range
    return p[indexes-1]                 # Subtract 1 since primes array is base 0 indexed

Test

print(superPrimes(200))
# Output: [  3   5  11  17  31  41  59  67  83 109 127 157 179 191]
DarrylG
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