I'm extremely confused.
for any odd number N greater than 3, N-1 and N+1 will both be even, hence not prime. I don't understand the bearing of this obvious fact with respect to the potential primality of N. All mersenne numbers are inherently odd (as they are a power of 2 minus 1). What does this prove? Your step 3) below factors A(O), how?
----- Original Message ----- From: "Dipl.-Ing. K.Kudiabor" <[EMAIL PROTECTED]>
To: "The Great Internet Mersenne Prime Search list" <[EMAIL PROTECTED]>
Sent: 2004-07-21 2:36 PM
Subject: Re: [Prime] Re: You no longer need Lucas-Lehmer Double...
Subject: [Prime] Re: You no longer need Lucas-Lehmer Double...
A repeat of my proposal (now in email-format) :Given M8=2^31-1= 2 147 483
647 =A(0): Prove and certify the primality, so that all of us can check
and verity at sight. Here is the proposal.
1) A(0-1) = 2 147 483 646 = 2 x 3 x 3 x 7x 11 x 31 x 151 x 331;
B(0)=331
A(0 ) = 2 147 483 647
A(0+1) =2 147 483 648 = 2^31 (these prime factors are easily verifiable)
A(0 ) is prime, certified by A(0-1), A(0+1) and B(0) below. (One and the same algorithm must be used to factorize the sequential integers A(0-1) to A(0+!)
2) In case B(0 ) = 331 is too large for sight prime verification this
iteration would be necessary:
B(0-1) = 330 = 2 x 3 x 5 x 11 (these prime factors are easily verifiable)
B(0 ) = 331
B(0+1) = 332 = 2 x 2 x 83 (these prime factors are easily verifiable)
B(0 ) is prime, certified by B(0-1) and B(0+1)
3) The Mersenne number M =2^29-1 = 536 870 911 = A(0) is patently no prime.
A(0-1) = 536 870 910 = 2 x 3 x 5 x 29 x 43 x 113 x 127 ( prime factors
verifiable)
A(0 ) = 536 870 911 = 233 x 1103 x 2089
A(0+1) = 536 870 912 = 2^29 ( prime factors verifiable)
4) The same Adjacent Prime factor Criterion (APC) can be used fo verify John
Findley's 7-million digit Mersenne: M41=2^24,036,583 - 1 =A(0). You'll save
that much time and resources for the usual independent verification.
http://www.mersenne.org
A(0-1)= M41 -1
A(0) =M41
A(0+1)= M41+1
5) And this rule is always true: The rightmost digit of any prime p=>11 is an element of the odd-number set nodd=[1,3,7,9] CAREFUL !! 21, 39, 57, 99 are composites, So the odd-number rule is only useful for a quick sight primality check of newly found mega-digit primes, for instance;
M40=2^20,996,011-1
= ..481331395421550326484866710969127787170820477533409300972948475231983471
676
653078163294714065762855682047
http://www.mersenne.org/prime6.txt
M41= 2^24,036,583 - 1 = ..49549332624134295037485542595520771846437818325642314252685868703980055603 1 269118412915067436921882733969407 http://mersenne.org/prime7.txt
Now to David A. Bartizal's question: Did I miss something subtle ?
Check No. 1) above . It is the main point. No. 5) is just a short-cut of your quotation All primes > 2 are odd numbers, but not all odd numbers are prime. I use the short-cut (note excluding odd number 5) to check GIMPS-Mersennes, Maybe somebody will give away a trick how to do that otherwise. Kodjo Kudiabor
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