Strong and weak primes: Difference between revisions

=={{header|Python}}==

Using the popular [http://www.numpy.org numpy] library for fast prime generation.

COmputes and shows the requested output then adds similar output for the "balanced" case where <code>prime(p) == [prime(p-1) + prime(p+1)] ÷ 2<code>.

<lang python>import numpy as np

def primesfrom2to(n):

# https://stackoverflow.com/questions/2068372/fastest-way-to-list-all-primes-below-n-in-python/3035188#3035188

""" Input n>=6, Returns a array of primes, 2 <= p < n """

sieve = np.ones(n//3 + (n%6==2), dtype=np.bool)

sieve[0] = False

for i in range(int(n**0.5)//3+1):

if sieve[i]:

k=3*i+1|1

sieve[ ((k*k)//3) ::2*k] = False

sieve[(k*k+4*k-2*k*(i&1))//3::2*k] = False

return np.r_[2,3,((3*np.nonzero(sieve)[0]+1)|1)]

p = primes10m = primesfrom2to(10_000_000)

s = strong10m = [t for s, t, u in zip(p, p[1:], p[2:])

if t > (s + u) / 2]

w = weak10m = [t for s, t, u in zip(p, p[1:], p[2:])

if t < (s + u) / 2]

b = balanced10m = [t for s, t, u in zip(p, p[1:], p[2:])

if t == (s + u) / 2]

print('The first 36 strong primes:', s[:36])

print('The count of the strong primes below 1,000,000:',

sum(1 for p in s if p < 1_000_000))

print('The count of the strong primes below 10,000,000:', len(s))

print('\nThe first 37 weak primes:', w[:37])

print('The count of the weak primes below 1,000,000:',

sum(1 for p in w if p < 1_000_000))

print('The count of the weak primes below 10,000,000:', len(w))

print('\n\nThe first 10 balanced primes:', b[:10])

print('The count of balanced primes below 1,000,000:',

sum(1 for p in b if p < 1_000_000))

print('The count of balanced primes below 10,000,000:', len(b))

print('\nTOTAL primes below 1,000,000:',

sum(1 for pr in p if pr < 1_000_000))

print('TOTAL primes below 10,000,000:', len(p))</lang>

{{out}}

<pre>The first 36 strong primes: [11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439]

The count of the strong primes below 1,000,000: 37723

The count of the strong primes below 10,000,000: 320991

The first 37 weak primes: [3, 7, 13, 19, 23, 31, 43, 47, 61, 73, 83, 89, 103, 109, 113, 131, 139, 151, 167, 181, 193, 199, 229, 233, 241, 271, 283, 293, 313, 317, 337, 349, 353, 359, 383, 389, 401]

The count of the weak primes below 1,000,000: 37780

The count of the weak primes below 10,000,000: 321749

The first 10 balanced primes: [5, 53, 157, 173, 211, 257, 263, 373, 563, 593]

The count of balanced primes below 1,000,000: 2994

The count of balanced primes below 10,000,000: 21837

TOTAL primes below 1,000,000: 78498

TOTAL primes below 10,000,000: 664579</pre>