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Old 2017-12-28, 10:02   #36
Feb 2017

3×5×11 Posts
Unhappy Falling on my sword

If it is too good to be true, it is too good to be true.

I have been found out by my lack of math training and hubris. For this I stand accused and am guilty. I will consider to leave this site voluntarily and won't post anything again under any name.

The algorith has false positives...apparently when 2^n-1 mod (n+2)= 1/2*(2^n-1)+1, which also happens to correspond to the first encountered mersenne non-primes, for which I could run the sagemath non-commercial software installed on my laptop. I did not pick this up the matrix table/grid that I was working with, which commenced at the first odd prime. The algorithm seemed to hold true for the first few hundred of odd numbers/primes and also seemed to hold for high prime numbers, but the false positives probably rubbishes the algorithm.

I also erred in claiming that the algorithm holds up to M34...the algorithmic relationship of the "mersenne odd number (dividend)" to the "odd number(prime)" in the matrix holds, but the tested prime (divisor) lags exponentially to the mersenne odd number part (dividend) in the modulo relationship. I conflated the dividend and the divisor in my claim w.r.t M34. This of course is a massive deficit, contrary to what I had claimed.

I could not find any case where the tested (odd) prime divisor returned a false value, so it might be that the "primality" function still holds.

The algorithm seems to hold for all non-prime divisors (composites), where the non-prime divisor is not in the form of 2^n-1, with 2^n-1 mod n+2, not equal to 1/2*(2^n-1)+1...(but this is not proven/verified), that is, apparently for the common composite odd number dividors divisible by 3, 5, etc.

So I stand accused and is deserving of any scorn for my outlandish claims never-the-less. I was called "dishonest" on this site before with a previous "algorithm", so I probably deserve this label, very certainly for due diligence.

In my defense I can only say that I am a hobbyist, and that I really thought I had hit onto something big. As far as I could tabulate the matrix table -from which I derived the "modulo formula", the results returned true. The consistency of the table- modulo ~ mersenne odd numers (starting at 1) vs odd numbers (starting at 3), also seemed intrisically logical and consistent, for the first few hundred odd number (modulo divisors).

The algorithm is this:

For x=n (n being an element of the set of odd (positive) number/integers, n=>1), (2^n-1) mod (n+2) is congruant to (n+1)/2 for all odd prime numbers, and non-congruant for all composites (barring false positives!!!!).

Thats it!

The relationship holds up at least (as tested using sagemath) with respect to the dividend/divisor relationship of 1,257,785/1,257,787, for what it is worth.

That is it, that is the algorithm.

I feel ashamed and have made a big fool of myself and the readers by wasting their time. For this I apologise.
gophne is offline   Reply With Quote