@qtip2001/

# Advanced Prime Detection

## Requires a very high IQ (200+)

Files
• main.py
main.py
```1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
```
```# Quentin Bishop
# 29 Nov 2018
import random
from time import time

def trial(n, d, r):
a = random.randint(2, n-1)
val = pow(a,d,n) -1
if val%n == 0:
return True
for s in range(0, r):
val = pow(a,d*(2**s), n) + 1
if val%n == 0:
return True
return False

def dr(n):
r = 0
n= n-1
while (n)%2 == 0:
n = n//2
r += 1
d = n
return(d,r)

def is_prime(n):
if n%2 == 0:
return False
d,r = dr(n)
for k in range(10):
if trial(n,d,r) == False:
return False
return True

def is_square(apositiveint):
x = apositiveint // 2
seen = set([x])
while x * x != apositiveint:
x = (x + (apositiveint // x)) // 2
if x in seen: return False
return True

def factorize(n):
x = int(n**0.5)
while True:
if is_square(x**2-n):
return (x+int((x**2-n)**0.5), x-int((x**2-n)**0.5))
x+=1

def run_trial(e):
t0 = time()
p1 = 2**(e-1)+1+random.randint(1,2**(e-6))*2
while not is_prime(p1):
p1+=2
p2 = 2**(e-1)+1+random.randint(1,2**(e-6))*2
while not is_prime(p2):
p2+=2
t1 = time()
#print('Seconds to generate primes: %f' %(t1-t0))
m = p1*p2
t2 = time()
print(factorize(m))
t3 = time()
return(t1-t0, t3-t2)
#print(f)
#print('Seconds to factorize: %f' %(t3-t2))

def run_multiple_trials(e):
pt = 0
ft = 0
for x in range(10):
trial = run_trial(e)
pt += trial[0]
ft += trial[1]
print(pt/10, ft/10)

run_multiple_trials(32)```