... Putting aside that there is no solution for the prime 2, the first few cases where it does not hold are p = 101, 173 and 367. (Nice try though!) Mark...
17927
jcmtnez90
Apr 9, 2006 11:37 pm
You are right, therefore I will change the conjecture to every prime greater than 2....
17928
Mark Underwood
marku606
Apr 10, 2006 12:19 pm
As per Goldbach, it seems very likely that any even number greater than two can be written as the sum of two primes. But these fun aberrations might hold as...
17929
Mark Underwood
marku606
Apr 10, 2006 2:38 pm
... than ... aberrations ... calls. ... Correction, I meant: Any even number greater than two can be written as the sum of two primes whose (*non negative*)...
17930
mikeoakes2@...
mikeoakes2
Apr 10, 2006 4:53 pm
... That was for the form a^2 + 2*b^2 + 3*c^2. It's interesting to explore also the exceptions to the form a^2 + b^2 + 2*c^2 (*) In this case there *does*...
17931
Jacques Tramu
echolalie
Apr 10, 2006 7:49 pm
... From: <mikeoakes2@...> To: <primenumbers@yahoogroups.com> Sent: Monday, April 10, 2006 6:52 PM Subject: [PrimeNumbers] Re: all primes as 1a^2 + 2b^2...
17932
Mark Underwood
marku606
Apr 11, 2006 6:01 pm
As we know, all primes can be expressed in the form x^2 + y^2 or x^ + 2y^2 or x^2 - 2y^2. But what happens if we allow only the forms ax^2 + by^2, a,b ...
17933
Paul Underwood
paulunderwooduk
Apr 11, 2006 9:39 pm
... Thanks very much, Jean, for a significant speed up over version 3.6.2 on some P4s at 2.6M bits (321). For example, at 2.5GHz I have noticed the times for a...
17934
Mark Underwood
marku606
Apr 13, 2006 7:14 pm
A couple of weeks ago I stumbled upon something interesting when I was searching for prime polynomials, and luckily I just remembered it. So here it is before...
17935
Mark Underwood
marku606
Apr 14, 2006 1:37 am
After cursory inspection a couple of partial generalizations: (n^2)x^2 + nx + k produces the exact same prime factors as (n^2)x^2 + n^2x + k + (n^2-1)/4 (n...
17936
mikeoakes2@...
mikeoakes2
Apr 14, 2006 10:38 am
... Mark: Substituting y = n*x, the polynomial (n^2)*x^2 + n*x + k becomes y^2 + y + k Substituting z = n*x + (n-1)/2, the polynomial (n^2)*x^2 + (n^2)*x + k +...
17937
Mark Underwood
marku606
Apr 14, 2006 3:47 pm
... obtained by PariGP's polredabs() function. ... Thank you Mike! Truly the veil has been lifted and I can now see the forest despite the trees :o I feel like...
17938
Kermit Rose
kermit1941
Apr 14, 2006 5:07 pm
From: primenumbers@yahoogroups.com Date: 04/14/06 03:42:00 To: primenumbers@yahoogroups.com it. First, I saw that 25x^2 + 5x + 958313 has no prime factors...
17939
Jens Kruse Andersen
jkand71
Apr 14, 2006 5:23 pm
... Suppose an odd prime p does not divide a. Then p can be a prime factor of ax^2+bx+c iff the discriminant D = b^2-4ac is a square modulo p. Consider the...
17940
Bryan
beyastard
Apr 14, 2006 5:43 pm
When you think you may have found some new prime numbers, how can you verify that they're not already known and, if not known, where would you report or submit...
17941
Edo Rajh
edorajh
Apr 14, 2006 6:00 pm
To make to the top 5000 list today a prime must have 68541 digits....
17942
Peter Kosinar
pkosinar
Apr 14, 2006 6:48 pm
Hello, ... Yes, they would... but there is a small catch. Let me quote the header of the all.txt file: * (The 5,000 largest known primes) *...
17943
Lélio Ribeiro de P...
lelio_73
Apr 14, 2006 6:53 pm
... you ... would ... small ... from ... numbers ... As Edo Rajh pointed out, to make the top-5000 list today, a prime must have 68k+ digits. The list you see...
17944
Edo Rajh
edorajh
Apr 14, 2006 7:45 pm
You might want to consider joining one of the many projects that search for big, top-5000 primes. You can check here which projects are top projects by number ...
17945
w_sindelar@...
Apr 15, 2006 2:10 pm
I cooked up a simple exercise for myself and found to my surprise that there exist unique even integers with a remarkable (to me) property. I can't think of a...
17946
Kermit Rose
kermit1941
Apr 15, 2006 6:15 pm
I'm looking for clear, concise explanations of the various methods for factoring integers. Kermit < kermit@... >...
17947
Jacques Tramu
echolalie
Apr 15, 2006 7:41 pm
To: <primenumbers@yahoogroups.com> Sent: Saturday, April 15, 2006 8:14 PM Subject: [PrimeNumbers] query on factoring methods ... One method is : procedure...
17948
Kermit Rose
kermit1941
Apr 16, 2006 3:00 pm
From: Jacques Tramu Date: 04/15/06 15:42:08 To: Kermit Rose; primenumbers@yahoogroups.com Subject: Re: [PrimeNumbers] query on factoring methods To:...
17949
Bob Gilson
bobgillson
Apr 16, 2006 3:39 pm
Carl Pomerance's published papers on factoring gives clear, concise methods of factoring. These are available on the Internet, and do not involve trial...
17950
Deapesh Misra
deapesh
Apr 16, 2006 3:59 pm
... * "Prime numbers: a computational perspective", Springer-Verlag, 2001 {book} * A Tale of Two sieves - Carl Pomerance {article} * Integer Factoring - Arjen...
17951
Michael S
michael971
Apr 20, 2006 3:02 pm
I am trying to figure out if X*X + 1 are primes or not those ending in the digits 2 are not since (10X+2) or (10x+8) squared end in 4 and if you add one the...
17952
Jose C. Martinez
jcmtnez90
Apr 20, 2006 7:14 pm
I wanted to know how are called those primes numbers that when are readed from left to right and from right to left both number are primes. For example 13-31 ...
17953
Jud McCranie
judmccr
Apr 20, 2006 7:29 pm
... They are called "reversible primes"....
17954
Ronny Edler
ronny_edler
Apr 20, 2006 7:30 pm
... They are called palindromic primes. See: http://primes.utm.edu/glossary/page.php/PalindromicPrime.html http://mathworld.wolfram.com/PalindromicPrime.html ...
17955
Ronny Edler
ronny_edler
Apr 20, 2006 7:58 pm
Oh - read too hasty... Jud is right - nevertheless the palindromic primes are a proper subset of the reversible primes. :) Ronny...
