Proth's Theorem (1878): Let n = h. 2^k + 1 with 2^k > h. If there is an integer a such that a^[(n-1)/2] = -1 (mod n), then n is prime. Examining small...
A couple folks have asked me to add a RSS feed (really simple syndication) to my database, so as an experiment I did so with the top 20 lists, e.g., ...
Dirk Augustin has set a 12-tuplet record at 50 digits: 8486221*107# + 4549290807806861 + 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42 Records are kept at...
Longer patterns start at 107 (length 7), 14633 length 8), 38089 (length 9) If you beleive the extended Dirichlet confecture, there are arbitarily long...
For prime(N)if gap == 1 && N % 10 == 1 then N % 15 = 11 always. && N % 10 == 7 then N % 15 = 2 always. && N % 10 == 9 then N % 15 = 14 always. For all prime 2...
For prime(N)if gap == 1 && N % 10 == 1 then N % 15 = 11 always.eg.,11, 41,71..... && N % 10 == 7 then N % 15 = 2 always.eg.,17, 107,137... && N % 10 == 9...
... mistake ... this. I assume by gap==1 you mean that N and N+2 are both primes. Let's look at your first example: N%10==1 if N%10==1 then N%15==(1,6 or 11)....
... That should be 39089. The first length 15: 64316477382794687 + 0 = 64316477382794687 (Prime) 64316477382794687 + 50 = 64316477382794737 (Prime) ...
I'm slowly building my factoring subroutines. I can factor numbers in the 12 digit range pretty quickly now, but it still
took over a minute to find a factor...
I can factor numbers in the 12 digit range pretty quickly now, but it still took over a minute to find a factor of 10^15 + 3. Why so long? It takes me 24 ms...
hecht
hecht@...
Jun 3, 2006 1:44 pm
18114
Hi everybody... Apparently there is a famous conjecture that every even number greater than two is the difference of two primes. 1st question: Does this...
huevon
elmerohuevo@...
Jun 3, 2006 9:58 pm
18115
... The Polignac conjecture is even stronger: "All" even numbers can be written as a difference of primes in infinitely many ways. Josechu Thanx, ... ...
... For numbers in that range (fewer than 64 bits), I wouldn't use HIT or any other such package. Just use the native data types. Also, Shank's method is...
... Now I've decomissioned my PPro/200, I don't have a machine slow enough to measure my native double reimplimantation of Lenstra's (LIP) version of Shanks'...
Thank you, Josechu and Conrad. That put me on the track. The de Polignac conjecture (he was a French mathematician of the 19th Century) is that all even ...
huevon
elmerohuevo@...
Jun 4, 2006 2:09 pm
18119
I started with this question: It is possible to find a number "k" that: 6k+1 returns a prime, in a way that we are sure of it primality, with no need of...
... Indeed you can. k=1, k=2 and k=3 are good examples! Bernardo Boncompagni ________________________________ "Wars not make one great" Yoda When's who A...
Message: 2 Date: Sun Jun 4, 2006 10:31 am (PDT) From: "develator81" develator81@... Subject: Trying to find when 6k+1 returns a prime I started with this...
Hi, Please refer to my communication of Oct.17,2004 to Yahoo prime number group on the subject of "Prime Structure" where I have discussed the occurrence of ...
In the late forties Mills proved [Mills47] that: Mills' Theorem: there is a real number A for which [A^3^n] is always a
prime (n = 1,2,3,...). I read that this...
Hi dudes, Can anyone say. Inorder to innovate some method for factorization and primality testing.(most efficient) Which one is the best way? Go up with the...
All: We're naming our new dog "Sophie Germain" and we were wondering about the correct pronunciation of the name. I think we've got a handle on Sophie, but...
... One would presume it's the same way as in Paris Saint Germain. In Kirshenbaum ASCII IPA, it's probably /Z@,m&~/ or /ZR,m&~/ Phil () ASCII ribbon campaign...
If I wrtie a long function definition in PARI/GP how do I save it for later use? This seems like an obvious question, but I just wrote at ratherlong script...
... for later use? This seems like an obvious question, but I just wrote at ratherlong script and I can't fiugre out how to save it! Sorry if this is an...
... a) Write it in a text editor instead. Save it and use \r to read it in. b) Use emacs. Phil () ASCII ribbon campaign () Hopeless ribbon campaign /\...
