Re: Mersenneplustwo project - something odd???

From: James Wanless (james_at_grok.ltd.uk)
Date: 08/13/04 

Date: Fri, 13 Aug 2004 16:23:05 GMT

Bart Goddard wrote:
> James Wanless wrote:
>
>
>>James Wanless wrote:
>>
>>>I _think_ 2^2281+1 is divisible by 6556086699
>>>The reason I say "think" is because it's actually of the form 2kp+3
>>>(sic) [apparently]
>>>I'd really appreciate a second opinion...
>>>J
>>>
>>>http://bearnol.is-a-geek.com/Mersenneplustwo/Mersenneplustwo.html
>>
>>Similarly [or at least according to 'calc'] 2^2203+1 is divisible by
>>39657 (!) - which again is apparently of form 2kp+3
>>Have I discovered a bug, a mathematical oversight, or are my 'puter(s)
>>just going screwy???
>
>
> Note that there are three smaller divisors of 2^2281+1:
>
> 3, 22811 and 95803. The second two of the form 2kp+1, while 3 is not.
>
> If you multiply these three divisors together, you get 6556086699.
>
> You have not discovered a new divisor, but only the product of the
> previously known divisors.
>
>
> Likewise, 3 x 13219 = 39657. Same problem.
>
> Bart
>
You are Brilliant!! Thanks ever so much!