Re: More on triangle numbers and primes!

>>I have read somewhere that an odd perfect
>> The 10 is probably an anomaly because it comes right
>>after 9, the start of my sieve, but why 136 not >>showing? >> Maybe I missed that in one of your proofs!

>My proofs don't cover 136, since 136 isn't perfect and >136 isn't odd.
>136 is a triangle number T(17), and 10 is T(5). Are >there any more
>missing even numbers? (You might try finding the prime >factorizations
>of the even numbers that are missing. Both are a power >of 2 times a
>prime; I don't know whether that's significant, though.)

I also discovered about 136 is, if you multiply its
deficient integers instead of add--
1*2*4*8*17*34*68 = 136^3
I don't know if that means anything either!

>> BTW: Odd perfect numbers have been checked up
>> to 10^300 -- Math world. More than likely they
>> don't exist but they are still checking higher
>> because there is no sound proof that there isn't
>> one!

>I was aware of searches up to this size, but you said >there was a proof
>that there are no odd perfect numbers, which is vastly >different from
>having no proof that there is an odd perfect number!

>--- Christopher Heckman

Maybe I explained it wrong but here is the one of my
previous post statement--- I high lighted in ( ).

>>I have read somewhere that an odd perfect
>>number (does not exist) but (they cannot prove)
>>that it doesn't. So if all the even perfect
>>numbers do not exist right of the (|) then
>>the first odd composite =>9 not found and not being
>>prime might just be the 1st odd perfect number.
-------------------------------------------------------
Just an added statement about the sieve of t(n)-t(y)
where n>y.
This is inefficient I know but it still rips quite fast.
What is interesting about this sieve is, you
build a data file or array with the first entries --
9,3 ===== t(4)-1, 3 = constant add to t(4)-1
14,4 ----etc.
20,5
27,6
35,7
.. etc

Run the 9's set as deep as the size primes you
want to extract or the limit of the array or file you have for storage. In an array or file plug the blank
spots by identifying the location as a prime or if an
even # blank spot then eliminates that location #.

Then run the next set [14,4] etc.
After you run and save all sets, retrieve array or file
for listing out the primes.

This will just display all primes > 7, and eliminates
all 2^>3 and the few perfect #.(also 10 and 136)

This really rips but the draw back is all the data required for retrieval and storage becomes a problem
for a large list of primes.
Although it is very easy to create the data, just that
the overhead restricts the size of your prime output.

Just an interesting exercise anyway!

Dan
.

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