Re: A benchmark comparing ECM and triangle number factoring.

dan73 <fasttrack2a@xxxxxxx> writes:
As a test I chose 2 equal length primes of 309
digits each with their ratio close to but less than (2).

Close? That's an understatement.

You are right--- a (1) followed by 150 9's after
the decimal point.
As you decrease the number of 9's(replaced with
any other digit)between any ratio of two primes it
becomes harder and harder to factor the semi-prime
with my method.


Here are the two primes with 309 digits each that are
the factors of the semi-prime I used in the benchmark test!

179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137859

359538626972463181545861038157804946723595395788461314546860162315465351611001926265416954644815072042240227759742786715317579537628833244985694861278837891845969618258052648190195896371115988140369645820920259833633655409693853416059037125722165175517329013747430538531505228028427798462090857128884811860889

? p2/p1*1.
1.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999386119313546687420675910306427450670341023326510669172174971676004261248769726981174221976630359748660245331869923620252889747947569931153601505605283235542419573722249916413759437067985048206303092414988913110569939475994169164368793444261530785312

Dan

Ps
ECM is still cranking after 3hrs and 15 minutes and >still
only showing that the 617 digit is a composite.
What gives?

ECM will factor arbitrary composites. Your composite is >far from arbitrary.
Can your algorithm factor RSA120? Nowadays, ECM can.
(Not that you'd
want to, of course.)

No, not with just one computer I would not even attempt
it. I just did this as a benchmark test.
With many computers starting at different sums and
indexes it could be realized. Running so as to not overlap one another.

Normally ECM will handel smaller semiprimes of this
nature but my method still wins out against ECM for
these type of semi-primes.(ratio slightly <> 2)

As I read somewhere as an analogy to factor rsa2048 it
would be like searching for one discrete grain of sand
in the universe and that grain of sand if found would be
one of the factors.

Phil
--
The fact that a believer is happier than a sceptic is >no more to the
point than the fact that a drunken man is happier than >a sober one.
The happiness of credulity is a cheap and dangerous >quality.
-- George Bernard Shaw (1856-1950), Preface to >Androcles and the Lion
.

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