I know that kv is only prime if k=1
What i mean is, since kv must be prime to let 2^kv-1 be possible prime, only one value
of k can let kv prime, value of 1, so only k=1 can 2^kv-1 be prime, so v can only be
factor of one Mx
*********** REPLY SEPARATOR ***********
On 20-3-02 at 6:52 Steve Harris wrote:
>Torben, I noticed something along those lines long ago: the first
>non-prime
>Mersenne number is M11 which factors to 23 times 89. The very next
>non-prime
>Mersenne number is M23, and M89 is also not prime. It occurred to me then
>that possibly Mx is never prime if x is a factor of a Mersenne number, but
>it was just an observation and I never got around to pursuing it. If so,
>then it would (although only very slightly) reduce the number of candidates
>to be tested. So I am just as curious as are you.
>
>Jeroen, I am wondering about your phrase "if kv is not prime then 2^(kv)-1
>isn't also" because kv is never prime, it has factors k and v (unless k=1,
>of course), and 2^(kv)-1 always has factors 2^k-1 and 2^v-1. I don't know
>if
>you meant something else or if I just misunderstood you. Sorry if that's
>the
>case.
>
>Regards,
>Steve Harris
>
>
>
>-----Original Message-----
>From: Jeroen <[EMAIL PROTECTED]>
>To: [EMAIL PROTECTED] <[EMAIL PROTECTED]>
>Date: Tuesday, March 19, 2002 8:12 PM
>Subject: Re: Mersenne: Factors aren't just factors
>
>
>>to find the value v where prime p is a factor of 2^v-1
>>
>>tempvalue = p
>>count = 0
>>while tempvalue != 0
>>{
>> if tempvalue is odd
>> {
>> shiftright tempvalue
>> count++
>> }
>> else
>> {
>> tempvalue+=p
>> }
>>}
>>
>>if the count is a primenumber then p is thus a factor of a mersenne prime
>>if the count is not a primenunber it isn't
>>if p is a factor of 2^v-1 then it is also a factor of 2^(2v)-1
>>or just 2^(kv)-1 for all value of k are integers above 0
>>if kv is not prime them 2^(kv)-1 isn't also, so each prime can only be a
>factor of one mersenne numer or 0 mersenne numbers
>>the first question is now simple to solve, just find the 2^v-1 where Mx is
>a factor of
>>
>>
>>
>>*********** REPLY SEPARATOR ***********
>>
>>On 20-3-02 at 0:21 Torben Schlüntz wrote:
>>
>>>Just of curiosity:
>>>
>>>Has it ever happened that a factor for Mx later has proved to be a
>>>mersenne prime itself?
>>>
>>>Has the same factor been a factor for two different Mx and My?
>>>
>>>In my humble oppinion both questions answers No; but GIMPS could have
>>>proved otherwise.
>>>
>>>Anyway, it must exist a great deal of low primes; which by now never can
>>>become mersenne factors (by reason: 2kp+1). So with two types of primes,
>>>those that are mersenne factors and those that never can be, do we have
>>>any means of distinguish them?
>>>
>>>
>>>Happy hunting
>>>tsc
>>>
>>>Btw: (M29 mod 1 + M29 mod 2 +......+ M29 mod 32) = 233 which is 1.
>>>factor of M29
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>>
>>
>>
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>>
>
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