fasttrack2a@xxxxxxxxxxxxx wrote:
> 1.97392088021787172376689819997523022706273988144815812528266987524400896448384104860035468074371044636480518275480462881555446962440600934552212353559703953219807997124131512611430120824656806575617387055386843298793331430380890774705235588276405165211633868250311840966196377465400661525333422087179017429295464019007160378918434879852438537690965863877456852147796433508362786493289138181812512380388703346821553105331495491731406920393436095466313240290182848436216333675904731787458644080194865355978580202996296272167583771329489901198337595619561182119709014789080879394109205379190285092351203383438007891921409e+617
>
> Why are these types of composites with only 2 prime factors of
> equal length and the fact that they are (very) easy to factor?
>
> The number of these composites with the above characteristics
> probably ---->oo.
>
> The first sentence holds the key! ;-)
>
> Dan
I tried this composite on Dario Alprens' factoring web site using the
elliptic curve method and it starts the primality check on the first
prime of 309 digits just after the first curve.
It looks as if the eliptic curve method is related to the triangle
numbers in as much it is a simple factorization if the composite
with equal length of two factors whos' differnence from the first
triangle
number > than itself is also a triangle number.
Which supports my belief that any two primes of equal length that
make up a composite whos' ratio is <> 2 but very close to (2)
will be very easy to factor.
The larger the composite and the variation of 2+ or 2- in the ratio
of the 2 primes becomes <> then 2 then the factorization becomes
that much more difficult.
Dan
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