Re: Nice number (was: Japanese voltage)
> > I still don't get it. > > > > ~Grauw > > > > Why aren't we surprised ??? > > > Sighhh, talking about a completely useless message !! > You could have cut almost the entire message. > No wonder that the bandwith of the Net is getting to small. I was aware of that. Still I thought the message had some use. Somehow I don't remember the use anymore... ~Grauw -- >< email me: [EMAIL PROTECTED] or ICQ: 10196372 visit the Datax homepage at http://datax.cjb.net/ MSX fair Bussum / MSX Marathon homepage: http://msxfair.cjb.net/ >< MSX Mailinglist. To unsubscribe, send an email to [EMAIL PROTECTED] and put in the body (not subject) "unsubscribe msx [EMAIL PROTECTED]" (without the quotes :-) Problems? contact [EMAIL PROTECTED] (www.stack.nl/~wiebe/mailinglist/)
Re: Nice number (was: Japanese voltage)
Laurens Holst wrote: > > By the way, the inverse is not always true: If the number of binary > digits > > is prime, is the number itself is not guaranteed to be prime. > Example: > 2047. > > > > Bye, > > Maarten > > I still don't get it. > > ~Grauw > Why aren't we surprised ??? Sighhh, talking about a completely useless message !! You could have cut almost the entire message. No wonder that the bandwith of the Net is getting to small. David -- "One difference between SuSE and Red Hat is that the former operates in a country where people don't sue each other over coffee being too hot." Linus Torvalds MSX Mailinglist. To unsubscribe, send an email to [EMAIL PROTECTED] and put in the body (not subject) "unsubscribe msx [EMAIL PROTECTED]" (without the quotes :-) Problems? contact [EMAIL PROTECTED] (www.stack.nl/~wiebe/mailinglist/)
Re: Nice number (was: Japanese voltage)
> > Of course it is. Not only 127 is prime, but also > >127=1+2+4+8+16+32+64. Knuth lovers may like to know that > >numbers in the form 11...b can only be prime if > >the number of digits is prime too (demonstration left to > >the reader). > > :) > > > Well, I'm a reader, so here comes a demonstation: > > Number N has D digits, which are all ones. > > Assume D is not a prime number. > So there are numbers A and B such that A*B=D (A>1,B>1). > > Now make numbers C[X], where C[X] is B ones followed by B*X zeroes. > For every X, the numbers C[X] are dividable by the number "B ones". > > The sum of C[0]..C[A-1] is N. > So N is also dividable by the number "B ones". > Since B>1, "B ones" is also greater than 1, so N is not prime. > > > Example: > > N = 255 = b (8 ones) > 8=4*2 (choice 2*4 is also possible) > > C[0] = 11b > C[1] = 1100b > C[2] = 11b > C[3] = 1100b > sum = b = 255 = N > > C[0]..C[3] are dividable by 11b (3), so the sum is too. And that sum is N, > so N is dividable by 3 and therefore not prime. > > > By the way, the inverse is not always true: If the number of binary digits > is prime, is the number itself is not guaranteed to be prime. Example: 2047. > > Bye, > Maarten I still don't get it. ~Grauw -- >< email me: [EMAIL PROTECTED] or ICQ: 10196372 visit the Datax homepage at http://datax.cjb.net/ MSX fair Bussum / MSX Marathon homepage: http://msxfair.cjb.net/ >< MSX Mailinglist. To unsubscribe, send an email to [EMAIL PROTECTED] and put in the body (not subject) "unsubscribe msx [EMAIL PROTECTED]" (without the quotes :-) Problems? contact [EMAIL PROTECTED] (www.stack.nl/~wiebe/mailinglist/)
Nice number (was: Japanese voltage)
At 04:29 PM 9/1/99 -0300, you wrote: > Of course it is. Not only 127 is prime, but also >127=1+2+4+8+16+32+64. Knuth lovers may like to know that >numbers in the form 11...b can only be prime if >the number of digits is prime too (demonstration left to >the reader). :) Well, I'm a reader, so here comes a demonstation: Number N has D digits, which are all ones. Assume D is not a prime number. So there are numbers A and B such that A*B=D (A>1,B>1). Now make numbers C[X], where C[X] is B ones followed by B*X zeroes. For every X, the numbers C[X] are dividable by the number "B ones". The sum of C[0]..C[A-1] is N. So N is also dividable by the number "B ones". Since B>1, "B ones" is also greater than 1, so N is not prime. Example: N = 255 = b (8 ones) 8=4*2 (choice 2*4 is also possible) C[0] = 11b C[1] = 1100b C[2] = 11b C[3] = 1100b sum = b = 255 = N C[0]..C[3] are dividable by 11b (3), so the sum is too. And that sum is N, so N is dividable by 3 and therefore not prime. By the way, the inverse is not always true: If the number of binary digits is prime, is the number itself is not guaranteed to be prime. Example: 2047. Bye, Maarten MSX Mailinglist. To unsubscribe, send an email to [EMAIL PROTECTED] and put in the body (not subject) "unsubscribe msx [EMAIL PROTECTED]" (without the quotes :-) Problems? contact [EMAIL PROTECTED] (www.stack.nl/~wiebe/mailinglist/)
