Re: Mersenne: mersenne prime +2

2003-04-06 Thread Brian J. Beesley
On Saturday 05 April 2003 20:33, Alexander Kruppa wrote: Bjoern Hoffmann wrote: Hi, I wondered if someone already have checked if the last mersenne numbers +2 are double primes? like 3+5, 5+7, 9+11, 11+13 or 824 633 702 441 and 824 633 702 443 regards Bjoern Mp + 2 is

Mersenne: mersenne prime +2

2003-04-05 Thread Bjoern Hoffmann
Hi, I wondered if someone already have checked if the last mersenne numbers +2 are double primes? like 3+5, 5+7, 9+11, 11+13 or 824 633 702 441 and 824 633 702 443 regards Bjoern _ Unsubscribe list info --

Re: Mersenne: mersenne prime +2

2003-04-05 Thread Alexander Kruppa
Bjoern Hoffmann wrote: Hi, I wondered if someone already have checked if the last mersenne numbers +2 are double primes? like 3+5, 5+7, 9+11, 11+13 or 824 633 702 441 and 824 633 702 443 regards Bjoern Mp + 2 is divisible by 3 for odd p and thus cannot be prime. Mp - 2 however can, in theory,

Re: Mersenne: mersenne prime +2

2003-04-05 Thread Brian J. Beesley
Hi, The _only_ incidence of 2^p-1 2^p+1 both being prime is p=2 yielding the prime pair (3, 5). Here's a proof by induction: Consider the difference between the second successor of two consecutive Mersenne numbers with odd exponents: (2^(n+2)+1) - (2^n+1) = 2^(n+2) - 2^n = 2^n * (2^2 - 1) =

RE: Mersenne: mersenne prime +2

2003-04-05 Thread Bjoern Hoffmann
Frank Anzalone [mailto:[EMAIL PROTECTED] wrote: 9 is Prime? like 3+5, 5+7, 9+11, 11+13 or this list was in a german article about the proof of infinite twin primes by Goldston and Yildirim. The 9 was marked as error of measurment for Pn+1 - Pn (log) Pn)^8/9

Re: Mersenne: mersenne prime +2

2003-04-05 Thread Joshua Zelinsky
Hi Brian J. Beesley wrote: The _only_ incidence of 2^p-1 2^p+1 both being prime is p=2 yielding the prime pair (3, 5). Here's a proof by induction: *snip* Another proof: 2^n+1 is prime easily implies n is a power of 2. The only power of 2 which is prime is 2. Regards, Josh Zelinsky [EMAIL