EPTI'm a lowly high school grade so I don't know things.
[Math] Prime number progression?! - Page 3
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Brethern
231 Posts
I'm a lowly high school grade so I don't know things. | ||
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dUTtrOACh
Canada2339 Posts
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Samhax
1054 Posts
On May 15 2011 08:44 dUTtrOACh wrote: The only way to test if it produces only prime numbers is to run divisibility tests on the answers for each case. You could write a program which can store the ridiculously large integers produced. Each will need to be tested for divisibility using modulus. Probably fairly time consuming. And when do you stop testing it? I dont think the op has the computer to do it, but i'm pretty the answer is no but you need a super computer to prove it or if he is lucky the first non prime number is not that big. | ||
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dUTtrOACh
Canada2339 Posts
On May 15 2011 08:46 Samhax wrote: I dont think the op has the computer to do it, but i'm pretty the answer is no but you need a super computer to prove it or if he is lucky the first non prime number is not that big. That's basically my point. | ||
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VIB
Brazil3567 Posts
On May 15 2011 08:44 dUTtrOACh wrote: You do realize "each case" is infinite right? If anyone ever solves this problem, it's not gonna be by making a computer bigger than infinite The only way to test if it produces only prime numbers is to run divisibility tests on the answers for each case.  | ||
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Samhax
1054 Posts
On May 15 2011 08:52 VIB wrote: You do realize "each case" is infinite right? If anyone ever solves this problem, it's not gonna be by making a computer bigger than infinite Maybe 2^127 -1 is not prime, if the op is lucky. But if 2^127 -1 is prime then you need for sure a super computer to prove it. | ||
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ZerGuy
Poland204 Posts
If a_n is the lowest non prime number in sequence A, then it's smallest dividor is larger that a_(n-1). That should save you the bothering with checking if A_6 is divisible by a small normal number | ||
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mcc
Czech Republic4646 Posts
There are other ways to prove things in math than to test every case, which in case of infinite sets is problematic  | ||
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Kong John
Denmark1020 Posts
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space_yes
United States548 Posts
[...] In mathematics, a Mersenne number, named after Marin Mersenne (a French monk who began the study of these numbers in the early 17th century), is a positive integer that is one less than a power of two: M_p=2^p-1 Some definitions of Mersenne numbers require that the exponent p be prime, since the associated number must be composite if p is. A Mersenne prime is a Mersenne number that is prime. It is known[2] that if 2p − 1 is prime then p is prime, so it makes no difference which Mersenne number definition is used. As of October 2009, 47 Mersenne primes are known. The largest known prime number (243,112,609 − 1) is a Mersenne prime.[3] Since 1997, all newly-found Mersenne primes have been discovered by the "Great Internet Mersenne Prime Search" (GIMPS), a distributed computing project on the Internet. [...] Many fundamental questions about Mersenne primes remain unresolved. It is not even known whether the set of Mersenne primes is finite. The Lenstra–Pomerance–Wagstaff conjecture asserts that, on the contrary, there are infinitely many Mersenne primes and predicts their order of growth. It is also not known whether infinitely many Mersenne numbers with prime exponents are composite, although this would follow from widely believed conjectures about prime numbers, for example, the infinitude of Sophie Germain primes congruent to 3 (mod 4). A basic theorem about Mersenne numbers states that in order for Mp to be a Mersenne prime, the exponent p itself must be a prime number. This rules out primality for numbers such as M4 = 24 − 1 = 15: since the exponent 4 = 2×2 is composite, the theorem predicts that 15 is also composite; indeed, 15 = 3×5. The three smallest Mersenne primes are M2 = 3, M3 = 7, M5 = 31. While it is true that only Mersenne numbers Mp, where p = 2, 3, 5, … could be prime, often Mp is not prime even for a prime exponent p. The smallest counterexample is the Mersenne number M11 = 211 − 1 = 2047 = 23 × 89, which is not prime, even though 11 is a prime number. The lack of an obvious rule to determine whether a given Mersenne number is prime makes the search for Mersenne primes an interesting task, which becomes difficult very quickly, since Mersenne numbers grow very rapidly. The Lucas–Lehmer primality test (LLT) is an efficient primality test that greatly aids this task. The search for the largest known prime has somewhat of a cult following. Consequently, a lot of computer power has been expended searching for new Mersenne primes, much of which is now done using distributed computing. | ||
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Manit0u
Poland17398 Posts
Example: (that's conjunction and implication if you don't get the notation used) p ^ q -> p Now, we asume that -> is false (0), and for it to be false the left hand side of it must be true (p ^ q) while the right hand side (p) must be false (you can't get false results from true things while you can get anything you want from false things). Then we get: 0 ^ q -> 0 Now we get to the problem, since no matter what we put in stead of q, our implication is going to be true (1), since in no way conjunction can be true if one of its elements is false, thus proving our original statement ( p ^ q -> p) to be a tautology, since it can never produce false results. Now all you need to do is create such test for your stuff. | ||
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Samhax
1054 Posts
Close the post :p | ||
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Mithrandir
United States99 Posts
These are Catalan-Mersenne Prime Numbers. http://en.wikipedia.org/wiki/Double_Mersenne_number#Catalan-Mersenne_number To the OP, please don't post unsolved problems and waste peoples' time. | ||
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ZerGuy
Poland204 Posts
On May 15 2011 09:03 Samhax wrote: Wikipedia give the larger Mersenne prime number 2^43 112 609 -1 discovered and 2^(2^127-1) -1 is bigger. So there is no way to prove it even with a super computer. Close the post :p Actually it's perfectly possible that this particular number can be proved as composed. It's just not known to be prime. On May 15 2011 09:08 Mithrandir wrote: This is an unsolved problem. These are Catalan-Mersenne Prime Numbers. http://en.wikipedia.org/wiki/Double_Mersenne_number#Catalan-Mersenne_number To the OP, please don't post unsolved problems and waste peoples' time. Was OP just a troll? So rude. | ||
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Sufficiency
Canada23833 Posts
Thus, I suggest you should compute a few iterations and check if they are primes. | ||
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Samhax
1054 Posts
On May 15 2011 09:08 ZerGuy wrote: Actually it's perfectly possible that this particular number can be proved as composed. It's just not known to be prime. I don't think so, because it's very hard top prove that a Mersenne number (2^p-1) is not prime when p is prime so if 2^127 -1 is prime, it's wil be tough. I'm not saying it's impossible but he will be really hard. | ||
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Mithrandir
United States99 Posts
On May 15 2011 09:12 Sufficiency wrote: I seriously doubt you have given a formula that always produces prime number. Thus, I suggest you should compute a few iterations and check if they are primes. The only iterations easily checkable have been checked, and they are prime. Like I said, nobody knows if this sequence (Catalan-Mersenne primes) always produces primes. Hell, this sequence is a subset of Mersenne Primes and nobody even knows if there are an infinite number of Mersenne Primes. | ||
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Mithrandir
United States99 Posts
On May 15 2011 09:08 ZerGuy wrote: Was OP just a troll? So rude. Probably a troll. By the time you discuss questions this hard, you know whether they're even solved. I have a hard time believing some high schooler/undergrad found this problem scribbled in their math textbook and wanted to know the solution. Solving this problem would be a huge achievement for a professional mathematician. | ||
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aoeua
United Kingdom75 Posts
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Samhax
1054 Posts
On May 15 2011 09:20 aoeua wrote: I have discovered a truly marvellous solution for this problem. Unfortunately, the post width here is too narrow to contain it. Haha Fermat quote, but Andrew Wiles did it! | ||
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