mersenneforum.org "New" primality test/check
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 2018-03-12, 19:58 #254 gophne   Feb 2017 3×5×11 Posts Hi CRGreathouse Thanx for the encouragement. I hope I can do justice to your positivity. I shall try to formulate my attempted "proof" carefully and mathematically as sound as possible. I will be delighted if the "proof" has any merit if somebody with more math knowledge and skills could take it the next level, but I am getting ahead of myself. I will be posting on this thread as I would not want to compromise the integrity and reputation of the forum by possibly posting a worthless, clueless attempted proof. If the proof should have any merit after analysis by the normal commentators, it would garner a life of its own I am sure. As for the primality test (for mersenne primes) it is formulaic in nature, so it is like proving the lemma for the lower mersennes, and then extending it to the rest of the set of mersenne numbers. My problem being that the "primality" check could well be too unwieldy at very high numbers. I do not have a good understanding of algorithm complexity and computation time concepts. I shall try my very best to validate whatever I post with due respect to the readers.
2018-03-12, 20:03   #255
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by gophne Thanx I will look at the links.
https://en.m.wikipedia.org/wiki/List...matical_jargon

https://en.m.wikipedia.org/wiki/Mathematical_proof

https://oeis.org/wiki/List_of_LaTeX_...atical_symbols

https://en.m.wikipedia.org/wiki/List...atical_symbols may as well.

Last fiddled with by science_man_88 on 2018-03-12 at 20:05

2018-03-12, 21:59   #256
CRGreathouse

Aug 2006

32×5×7×19 Posts

Quote:
 Originally Posted by gophne As for the primality test (for mersenne primes) it is formulaic in nature, so it is like proving the lemma for the lower mersennes, and then extending it to the rest of the set of mersenne numbers. My problem being that the "primality" check could well be too unwieldy at very high numbers. I do not have a good understanding of algorithm complexity and computation time concepts.
Think about it in four stages.

1. Define it precisely and unambiguously. Until you do this, you can't even be wrong.
2. Prove that your test holds for all primes (of the appropriate form). Once you do this you have a pseudoprimality test (but its value is still unclear).
3. Prove that your test fails to hold for all composites (of the appropriate form). Once you do this you have a primality test (but possibly a slow one).
4. Prove that your test runs in a (small) certain amount of time based on the size of the input and perhaps other characteristics.

There are in-between stages. Before you get to 3 you can perform random testing to show that your test fails for either all composites tested or a very high percentage. Before you get to 4 you can use heuristics or implementations to argue that it will be fast. Really you need to get to at least stage 2 before any of this matters though.

You don't need to get to 4 to be of value. BPSW is at 2, and Miller-Rabin is stuck there permanently. ECPP looks like it will be at 3 for the foreseeable future.

Last fiddled with by CRGreathouse on 2018-03-12 at 22:02

2018-03-12, 22:47   #257
chalsall
If I May

"Chris Halsall"
Sep 2002

24·5·7·17 Posts

Quote:
 Originally Posted by CRGreathouse Define it precisely and unambiguously. Until you do this, you can't even be wrong.
Along these lines, a very important thing to point out... It's perfectly OK to be wrong around here. It's a tough crowd, but being comfortable making mistakes is useful in making progress.

Some have run away from this forum because they thought they were being personally attacked. New ideas are welcomed, but are also open to deep analysis, and will be called stupid if they are. Nothing personal; deal with it.

It's a bit like the game of ruby, where you try to physically maim your opponent on the field, and then afterwards go and buy the guy a beer and laugh. Or the game of Go, where it's all fun and games until someone loses an eye.

 2018-03-13, 03:51 #258 gophne   Feb 2017 3·5·11 Posts Noted, thank you.
 2018-03-13, 04:01 #259 gophne   Feb 2017 A516 Posts Agreed. I have always accepted the critisisms I encountered on the forum in good faith. If I can also make use of a sporting analogy, it is like, as a novice tennis player, taking on Jimmy Connors, with Jimmy Connors sometimes feeling like hitting you on the head with the ball, for your audacity, and rightly so, if you cannot even get the ball to go consistently into the service court. You just have to hope that you do not come up against a John McEnroe, who will likely bash the ball boy over the head with his racquet, due to your doltishness! Last fiddled with by gophne on 2018-03-13 at 04:06 Reason: Spelling typo's!
2018-03-13, 04:04   #260
CRGreathouse

Aug 2006

32·5·7·19 Posts

Quote:
 Originally Posted by chalsall Along these lines, a very important thing to point out... It's perfectly OK to be wrong around here. It's a tough crowd, but being comfortable making mistakes is useful in making progress.
Yes!

We all make mistakes, and it's good to point out mistakes you see so they can be corrected.

 2018-03-17, 02:54 #261 gophne   Feb 2017 16510 Posts Dedicated to my daugter, Taryn I would like to make my attempt at a proof of the Twin Prime Conjecture on the 17/04/2018, which would be my daughter's birthday, hoping to make up for the bad days.
 2018-03-18, 08:31 #262 gophne   Feb 2017 2458 Posts "Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate." Leonard Euler, in G. Simmons, Calculus Gems, McGraw-Hill, New York, 1992 **************************************************************************************************** "Prime numbers have always fascinated mathematicians, professional and amateur alike. They appear among the integers, seemingly at random, and yet not quite: there seems to be some order or pattern, just a little below the surface, just a little out of reach." Underwood Dudley, Elementary Number Theory (Freeman, 1978) p.163 **************************************************************************************************** "Who would have imagined that something as straightforward as the natural numbers (1, 2, 3, 4,...) could give birth to anything so baffling as the prime numbers (2, 3 ,5, 7, 11, ...)?" Ian Stewart, "Jumping Champions", Scientific American, December 2000
2018-03-18, 16:18   #263
ATH
Einyen

Dec 2003
Denmark

1011111111102 Posts

Quote:
 Originally Posted by gophne I would like to make my attempt at a proof of the Twin Prime Conjecture on the 17/04/2018, which would be my daughter's birthday, hoping to make up for the bad days.
Considering how many great minds have worked on this for hundreds of years, most recently Professor Terence Tao, and Dr. James Maynard:

you might want to aim for 17/04/2030 or later to have any non infinitesimal chance at it.

 2018-03-18, 17:01 #264 science_man_88     "Forget I exist" Jul 2009 Dumbassville 100000110000002 Posts Another thing to keep in mind is the interconnectedness of conjectures. The twin prime conjecture and the goldbach conjecture are linked by goldbach partitions. So you'll have to potentially look out for provably false implications of conjectures against each other. Not that one will necessarily be false because of the other, just a thing to keep in mind.

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