User jaime montuerto - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T08:03:10Z http://mathoverflow.net/feeds/user/1717 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/5191/3-primes-in-ap-and-twin-primes-of-polynomials-forms-2x3-and-2x5 3 primes in AP and twin primes of polynomials forms \$2^x+3 and 2^x+5\$ Jaime Montuerto 2009-11-12T14:08:36Z 2010-09-13T05:18:53Z <p>1) Given primes of forms \$2^x + 3\$ and \$2^x + 5\$, what is the biggest x exponent for each to be prime? </p> <p>2) Given a 3 primes AP of the form \$(3, 2^x + 3, 2^[x+1] + 3)\$ with common difference of \$2^x\$, what is the biggest x exponent to produce the 3 primes AP?</p> <p>3) Given a 3 primes AP of the form \$(5, 2^x + 5, 2^[x+1] + 5)\$ with common difference of \$2^x\$, show that this 3 primes AP does not exist.</p> <p>4) Given a twin primes of the form \$(2^x + 3, 2^x + 5)\$, what is the biggest x exponent to produce a twin primes?</p> http://mathoverflow.net/questions/5323/infinitely-many-primes-of-the-form-2nc-as-n-varies/5348#5348 Answer by Jaime Montuerto for Infinitely many primes of the form 2^n+c as n varies? Jaime Montuerto 2009-11-13T14:03:13Z 2009-11-13T14:03:13Z <p>Hi, I believed that there are always an infinitude of primes in all forms of 2^n + c except c = 1 (fermat numbers). I don't have a proof though but gathering some data on my research of forms 2^x+3 and 2^x+5. I am interested the reason being that together they will produce infinite twin primes and prime arithmetic progression for (3,2^x+3,2^x+1 + 3), again just my belief and based on algorithm I am working on.</p> http://mathoverflow.net/questions/5323/infinitely-many-primes-of-the-form-2nc-as-n-varies/5348#5348 Comment by Jaime Montuerto Jaime Montuerto 2009-11-13T18:41:42Z 2009-11-13T18:41:42Z Thanks for this, now I concede about this result, of course my original question still holds. How big x exponent is? I would imagine it to be big. http://mathoverflow.net/questions/5191/3-primes-in-ap-and-twin-primes-of-polynomials-forms-2x3-and-2x5 Comment by Jaime Montuerto Jaime Montuerto 2009-11-13T14:13:42Z 2009-11-13T14:13:42Z Actually I believed that no biggest x exponent, I believed that it will be infinite of primes and my basis is an algorithm that is not necessarily modular arithmetic either. Q2 is about 3 primes in arithmetic progression (in fact the motivation in these set of question), that is starts with 3 whose common difference is a 2^x bit so 3, 2^x + 3 and 2^x+1 + 3, which I believed to have an infinite of set as well. http://mathoverflow.net/questions/5191/3-primes-in-ap-and-twin-primes-of-polynomials-forms-2x3-and-2x5 Comment by Jaime Montuerto Jaime Montuerto 2009-11-12T19:10:15Z 2009-11-12T19:10:15Z The interesting aspect of both forms is the distribution of primes (x exponent) on individual forms, as prime progression and the twin primes. I'm also interested in forms of primes that divides these forms. http://mathoverflow.net/questions/5191/3-primes-in-ap-and-twin-primes-of-polynomials-forms-2x3-and-2x5 Comment by Jaime Montuerto Jaime Montuerto 2009-11-12T19:07:33Z 2009-11-12T19:07:33Z Hi Sonia, I believed that both forms have an infinite primes. The 2^x +3 has 1/3 multiples of 7 whereas 2^x+5 has 1/2 multiples of 3. So in question 3, all even x exponent is multiple of 3 hence no AP of that form. I also believed to have infinite of twin primes in this form.