#(c) by Pat_and_I 2023/2024, Ferlach, Ă–sterreich
#program name: "find_any_factor"
#This program finds (probably???) one factor of any nonprime number
import math
import decimal
from datetime import datetime
import sympy
decimal.getcontext().prec=250
decimal.getcontext()
global c
#c=3
c=27071420938354717
fnd=False
global pgcd
pgcd=True==False #will be set to True, when you set variable "chk_one=True#==False"
global chk_one
chk_one=True#==False #delete the "#" between =True#==False and the program checks the numbers between a range
global tstall #test all chk_square_rest() calls. also, when a gcd was fnd
tstall=True==False
global called_chk_square_rest
called_chk_square_rest=0
global pcntcallsqurstfun
pcntcallsqurstfun=True==False
pcntcallsqurstfun=False
start_number=0
plus_range=2
print_diff=10**10
if chk_one:
pgcd=True
else:
tstall=False
pcntcallsqurstfun=False
start_number=3 #4797487931 #4378364971 #1298730659 #71710231 #5459603 #30563
plus_range=10**11
print_diff=10**8
if start_number%2==0:
start_number=start_number+1
def chk_square_rest(g1):
global c
global fnd
global pgcd
global print_one_number
global tstall
global called_chk_square_rest
if pcntcallsqurstfun==True:
called_chk_square_rest=called_chk_square_rest+1
if called_chk_square_rest%1000000==0:
print(called_chk_square_rest)
d1=math.isqrt(g1)
if d1*d1==g1 and d1>1:
h1=d1
m1=math.gcd(c,h1)
if m1>1 and m1<c:
if pgcd: print("gcd0: ",m1," g1: ",g1)
if tstall:
fnd=False
else:
fnd=True
return
else:
for i1 in range(0,2):
d1=d1+1
e1=d1*d1-g1
if e1<0:
print("........error 1: e1 is lower than null: ",e1)
f1=math.isqrt(e1)
if f1<1:
f1=1
if f1*f1==e1:
h1=d1+f1
m1=math.gcd(c,h1)
if m1>1 and m1<c:
if pgcd: print("gcd2: ",m1," g1: ",g1," digits(g1): ",math.trunc((math.log(g1)//math.log(10))+1))
if tstall:
fnd=False
else:
fnd=True
return
else:
h1=d1-f1
m1=math.gcd(c,h1)
if m1>1 and m1<c:
if pgcd: print("gcd1: ",m1," g1: ",g1," digits (g1): ",math.trunc((math.log(g1)//math.log(10))+1))
if tstall:
fnd=False
else:
fnd=True
return
else:
h1=math.gcd(c,e1)
if h1>1 and h1<c:
if pgcd: print("gcd: ",h1," g1: ",g1," digits (g1): ",math.trunc((math.log(g1)//math.log(10))+1))
if tstall:
fnd=False
else:
fnd=True
return
def chk_it_0():
global c
global fnd
global pgcd
global print_one_number
global tstall
global called_chk_square_rest
chk_square_rest(c)
if tstall:
fnd=False
if fnd:
return
e2=c
div2=1
while e2>0:
e2=e2//2
div2=div2*2
div2=div2//2
chk_square_rest(c*div2)
if tstall:
fnd=False
if fnd:
return
chk_square_rest(c*div2//4*3)
if tstall:
fnd=False
if fnd:
return
g2=math.isqrt(div2)
if g2**2!=div2:
g2=math.isqrt(div2*2)
mul_save_1=g2
mul_save_2=mul_save_1//4*3
if mul_save_2<3: mul_save_2=3
if mul_save_2<mul_save_1//2:
mul_save_2=mul_save_1//2
if mul_save_1>mul_save_2:
j2=mul_save_1
else:
j2=mul_save_2
for i2 in range(1,j2,2):
chk_square_rest(c*mul_save_1*i2)
if tstall:
fnd=False
if fnd:
return
chk_square_rest(c*mul_save_1*2*i2)
if tstall:
fnd=False
if fnd:
return
chk_square_rest(c*mul_save_2*i2)
if tstall:
fnd=False
if fnd:
return
chk_square_rest(c*mul_save_2*2*i2)
if tstall:
fnd=False
if fnd:
return
called_chk_square_rest=0
date_0=datetime.now()
if chk_one==True:
print("number to check: ",c)
pgcd=True
pcntcallsqurstfun=True
if not sympy.isprime(c):
print("c: ",c)
fnd=False
if c<2:
print("Number must be greater 2")
else:
pcntcallsqurstfun=True
chk_it_0()
else:
print("Number: ",c,"is prime")
print("count of calles for function 'chk_square_rest': ",called_chk_square_rest)
print("fnd: ",fnd)
else:
print("Start")
pgcd=False
count_of_is_not_prime_checked=0
if start_number<2 or start_number%2==0:
if start_number%2==0:
print("Number to start must be odd")
else:
print("Number to start must be greater 2")
print("No number was checked")
else:
for c in range(start_number,start_number+plus_range,2):
if not sympy.isprime(c):
if c%print_diff==1: print("#c: ",c)
count_of_is_not_prime_checked=count_of_is_not_prime_checked+1
fnd=False
chk_it_0()
if not fnd:
print("#c=",c," #not fnd")
#print()
else:
if c%print_diff==1: print("#c:",c,"count_of_is_not_prime_checked: ",count_of_is_not_prime_checked)
print("count of 'is not prime' checked=",count_of_is_not_prime_checked)
print("calculation time: ",datetime.now()-date_0)
