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 Showing results 1 to 25 of 29 Search took 0.03 seconds. Search: Posts Made By: juergen
 Forum: Math 2004-07-10, 23:01 Replies: 2 Views: 1,299 Posted By juergen Hi all, the sum over 1/p for all prime p < x... Hi all, the sum over 1/p for all prime p < x is called the reciprocal prime sum. If you are interested you will find further info on mathworld by searching for "mertens constant". regards ...
 Forum: Math 2004-07-06, 21:17 Replies: 2 Views: 1,299 Posted By juergen Hi all, sorry I missed something in the... Hi all, sorry I missed something in the second form. It is wrong :o( The first form is correct and the condition Sum (1.) >= 1. I am trying to learn something about numbers x for which this...
 Forum: Math 2004-07-04, 12:53 Replies: 2 Views: 767 Posted By juergen Sorry, I don't know the answer to your question,... Sorry, I don't know the answer to your question, but maybe you would like to read about Catalan's theorem which is the special case A=1. Catalan's theorem states that there is only one solution...
 Forum: Math 2004-07-04, 09:31 Replies: 2 Views: 1,299 Posted By juergen Search for a number theoretic function related to "prime divisor sums" Hi all, does anybody know a number theoretic function similar to the divisor sum, but which only sums up the divisors which are prime? For me a function would be interesting, which builds the ...
 Forum: Math 2004-05-15, 21:21 Replies: 23 Views: 1,961 Posted By juergen Can you really proof they are prime? Did you... Can you really proof they are prime? Did you check for all the factors? Why do you mix hex and decimal, btw? What was the largest prime you found? And sorry if it bores you, but I still would like...
 Forum: Math 2004-05-14, 20:17 Replies: 23 Views: 1,961 Posted By juergen I don't know the current size precisely, but it... I don't know the current size precisely, but it should be a little bit larger than 3000. The time it takes to find a larger one is not constant. But it is more than a minute. The sieving already...
 Forum: Math 2004-05-14, 12:40 Replies: 23 Views: 1,961 Posted By juergen I use the GMP-Routine to perform the modular... I use the GMP-Routine to perform the modular power calculation. This is pretty fast. It takes about 5 to 10 seconds on a Pentium III machine (666 Mhz) for a number which is about 3000 digits long. I...
 Forum: Math 2004-05-13, 18:00 Replies: 23 Views: 1,961 Posted By juergen I perform the trial divisions without further... I perform the trial divisions without further optimizations, but from the result I build a sieve. So I only perform the trial divisions on one candidate and build a sieve on the result of this...
 Forum: Math 2004-05-12, 22:01 Replies: 23 Views: 1,961 Posted By juergen Thank you very much for your hint. But if you... Thank you very much for your hint. But if you suggest something like this with a faint hint of a raised index finger then please make sure, that you also read all of the previous postings. I already...
 Forum: Math 2004-05-11, 21:02 Replies: 23 Views: 1,961 Posted By juergen The generic form is: p*n+1 where p is a... The generic form is: p*n+1 where p is a prime and n any natural number smaller than p. I guess that doesn't help a lot :o( Juergen
 Forum: Math 2004-05-04, 19:19 Replies: 23 Views: 1,961 Posted By juergen No I wrote this program myself. What is a... No I wrote this program myself. What is a PRP-Program by the way? and what does the program do you mentioned?
 Forum: Math 2004-05-03, 21:40 Replies: 47 Views: 7,823 Posted By juergen I really think that Euler was important, but do... I really think that Euler was important, but do you really think that he contributed more to the mathematical society then Gauss? Tho Gauss was more important than the three stated above, but of...
 Forum: Math 2004-05-03, 21:18 Replies: 23 Views: 1,961 Posted By juergen you are right. Miller Rabin is also such a... you are right. Miller Rabin is also such a compositeness test. Okay I guess thats clear, because it is just a variant of the fermat check. But maybe there is really no faster proof for compositeness...
 Forum: Homework Help 2004-05-02, 14:29 Replies: 2 Views: 1,594 Posted By juergen isn't this also what is called an ellyptic curve? isn't this also what is called an ellyptic curve?
 Forum: Math 2004-05-02, 13:51 Replies: 23 Views: 1,961 Posted By juergen Hi Cyclamen, to me the speed of such a test... Hi Cyclamen, to me the speed of such a test is more relevant than the safety. To proof my kind of numbers are prime I only need to perform a fermat check in combination with another step which...
 Forum: Math 2004-05-01, 10:35 Replies: 23 Views: 1,961 Posted By juergen Hi Cyclamen, Rabin only works for Mersenne... Hi Cyclamen, Rabin only works for Mersenne numbers, right? Oh, I looked at mathworld. It seems also be working for other primes :o) I guess it is much faster, isn't it? I will have a look at...
 Forum: Math 2004-04-30, 21:25 Replies: 23 Views: 1,961 Posted By juergen Primalty Test Hi all, are there any primalty tests which are faster than the fermat test for large numbers. The primalty test doesn't need to guarantee that a number is prime, it is already enough if I can...
 Forum: Math 2004-04-17, 12:19 Replies: 2 Views: 1,109 Posted By juergen Thank you for your suggestion. I don't know how... Thank you for your suggestion. I don't know how to add files here, so I put a pdf file on a web server you can download it on informatik.gmxhome.de/lcm.pdf (http://informatik.gmxhome.de/lcm.pdf) ...
 Forum: Math 2004-04-17, 10:42 Replies: 2 Views: 1,109 Posted By juergen least common multiple of numbers of the form a^x-1 Hello, what is the form of the least common multiple of numbers of the form v^(a*b*c) - 1, v^(a*b*d) - 1, v^(a*c*d) - 1 and v^(b*c*d) - 1 ? I know that it is not just the product...
 Forum: Math 2004-03-31, 22:05 Replies: 8 Views: 1,293 Posted By juergen Hi, I just read this. Does anybody know which... Hi, I just read this. Does anybody know which multi precision package is the fastest for large integer operations. Especially for "exponential residue" calculations (I don''t know if this is the...
 Forum: Math 2004-03-31, 21:19 Replies: 2 Views: 818 Posted By juergen Thank you very much Bob for this detailed answer!... Thank you very much Bob for this detailed answer! Do you think that 1.5 times it takes to perform a fermat test is also faster as what is done to proof the primality of a mersenne number? I guess...
 Forum: Math 2004-03-22, 21:38 Replies: 2 Views: 818 Posted By juergen performance of primalty check methods Hi all, I would like to know how fast primalty checks on real large numbers are (lets say for numbers of several thousands of digits). Are the primalty check methods (which proof that the number...
 Forum: Math 2004-03-16, 11:43 Replies: 1 Views: 1,100 Posted By juergen Hello all, I think to proof the first is... Hello all, I think to proof the first is easy. I think I could do this, but the others seem to be much more complicated. I try to figure out a rule here, but it seems not to be obvious to me. I...
 Forum: Math 2004-03-12, 00:01 Replies: 3 Views: 1,359 Posted By juergen Sorry I think thats exactliy how you derived this... Sorry I think thats exactliy how you derived this term?! Okay and of course there is a proof for the term above from wilson. There is a proof by wilson which states that p divides (p-1)! + 1 ...
 Forum: Math 2004-03-11, 20:29 Replies: 1 Views: 1,100 Posted By juergen general form of the multiplicative order Hi, are there any proofs about how the multiplicative order of numbers is calculated which include powers of primes? I put them in three categories: 1. Numbers of the Form p^n where p is a...
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