mersenneforum.org if p is prime, factors of 2^p-1? - Is it possible?
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2020-10-23, 05:32   #12
LaurV
Romulan Interpreter

Jun 2011
Thailand

2×4,463 Posts

Quote:
 Originally Posted by ONeil As you may or may not know all factors of prime numbers
...are the number itself and 1.
I think you only trolling, because I can't imagine a real person can behave the way yo do, so ignorant and so proud in the same time.
Take the advice other people gave you, and start learning something serious.

2020-10-23, 07:56   #13
ONeil

Dec 2017

3×72 Posts
This is super fast don't listen to them

I think they have the inside scoop.

I have found the machine for finding factors very fast. You need to make a list of many primes that are at least 10 digits long or greater than the average for factors found length. That's work I know, but when you are done you save time. Instead of a month processing your machine will come back in seconds with a factor. Now granted its about your list so you could miss a factor. At least if you miss a factor you could either make you list bigger or test that number to see if its prime here is the code. This code opens the list in a text file and uses it as mod against your test 2^p-1.

Here you can at least assess the average factor length:
https://www.mersenne.org/report_fact...xp_lo=12354673

Here is a small portion of my list inside the text file:
Quote:
 k = ( 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)
Code:
import timeit
while True:
p = int(input("Enter a prime number: "))
if p == 1:
print(p,"Come on man type a larger number or vote for Biden, because he is number 1")
continue
if p == 2:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 3:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 5:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 7:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 13:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 17:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 19:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 31:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 61:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 89:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 107:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 127:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 521:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 607:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 1279:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 2203:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 2281:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 3217:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 4253:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 4423:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 9689:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 9941:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 11213:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 19937:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 21701:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 23209:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 44497:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 86243:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 110503:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 132049:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 216091:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 756839:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 859433:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 1257787:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 1398269:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 2976221:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 3021377:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 6972593:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 13466917:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 20996011:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 24036583:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 25964951:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 30402457:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 32582657:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 37156667:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 42643801:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 43112609:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 57885161:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 74207281:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 77232917:
print(p,"The input 'p' produces a Mersenne Prime")
continue
elif p == 82569933:

print(p,"The input 'p' produces a Mersenne Prime")
continue

with open("C:\python37\k.txt",'r') as f:
primes = f.read().split("(")[1].split(')')[0].split(',')  # int list of primes
primes = [int(i.strip()) for i in primes]
for prime in primes:
if (2**p - 1) % int(prime) == 0:
start_time = timeit.default_timer()
print(prime)
print(timeit.default_timer() - start_time,'seconds')
break

Last fiddled with by ONeil on 2020-10-23 at 08:06

2020-10-23, 08:02   #14
Viliam Furik

Jul 2018
Martin, Slovakia

23×31 Posts

Quote:
 Originally Posted by a1call Meant 2^p-1 If for any prime p 2*p+1 | 2^p-1 Then 2*p+1 is definitely prime. The test is deterministic and computationally about as expensive as a PRP test.
This works with only k=1, thus if it divides 2p-1, it is definitely a prime factor.

Last fiddled with by Viliam Furik on 2020-10-23 at 08:04

2020-10-23, 08:04   #15
ONeil

Dec 2017

2238 Posts

Quote:
 Originally Posted by LaurV ...are the number itself and 1. I think you only trolling, because I can't imagine a real person can behave the way yo do, so ignorant and so proud in the same time. Take the advice other people gave you, and start learning something serious.
LaurV you are not a decent person you misquoted me you now have no respect from me you stoop very low indeed!

2020-10-23, 08:07   #16
Viliam Furik

Jul 2018
Martin, Slovakia

24810 Posts

Quote:
 Originally Posted by ONeil LaurV you are not a decent person you misquoted me you now have no respect from me you stoop very low indeed!
That is not a misquote, you are simply talking nonsense. Primes are not composite, that is their definition.

If you mean the Mersenne numbers... Those can be composite. Mersenne primes are a very rare special case of those numbers.

 2020-10-23, 08:07 #17 paulunderwood     Sep 2002 Database er0rr 25·109 Posts https://www.w3schools.com/python/python_sets.asp shows how to use sets in python. So you write something like: Code: known_mersenne_primes = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609, 57885161, 74207281, 82569933} and then you can use "in" like: Code: if p in known_mersenne_primes: print(p,"The input 'p' produces a Mersenne Prime")
2020-10-23, 08:13   #18
ONeil

Dec 2017

3·72 Posts

Quote:
 Originally Posted by paulunderwood https://www.w3schools.com/python/python_sets.asp shows how to use sets in python. So you write something like: Code: known_mersenne_primes = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609, 57885161, 74207281, 82569933} and then you can use "in" like: Code: if p in known_mersenne_primes: print(p,"The input 'p' produces a Mersenne Prime")
Thanks for the update Paul

2020-10-23, 08:20   #19
ONeil

Dec 2017

3×72 Posts

Quote:
 Originally Posted by Viliam Furik That is not a misquote, you are simply talking nonsense. Primes are not composite, that is their definition. If you mean the Mersenne numbers... Those can be composite. Mersenne primes are a very rare special case of those numbers.
This is what I said

Primes that make numbers from 2^p-1 which are not prime have factors that are prime, sorry for the confusion.

 2020-10-23, 08:24 #20 ONeil     Dec 2017 3·72 Posts A better way to phrase it would be: A composite number produced from a prime number using 2^p-1 does contain prime factors!
2020-10-23, 08:51   #21
Viliam Furik

Jul 2018
Martin, Slovakia

3708 Posts

Quote:
 Originally Posted by ONeil This is what I said
No, it is not. It is what you meant by it, but not what you actually said. But I understand now.

But there's a little sense in saying that. If the Mersenne number (2p-1) is prime, there is no discussion about factors. If it's not a prime, well, the only other option is that it is composite, which means it does have prime factors, but if it has strictly more than 2 of them (all the time, except for a very small part of those numbers), then the product of any two prime factors is also a factor, but a composite one.

 2020-10-23, 08:57 #22 paulunderwood     Sep 2002 Database er0rr 25·109 Posts It is of absolutely no use in reading in a list of factors. The factors of Mersenne numbers with prime exponents is disjoint: a prime dividing one Mp will not divide another Mq. Reading in from disk takes time too, It is better to loop over k for 2pk+1. For example M11 is (2*11+1)*(2*4*11+1) Going up to "10 digits" is pathetic. The guys (an gals) here go up to over 24 digits routinely. Last fiddled with by paulunderwood on 2020-10-23 at 09:05

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