Guest wrote:Tentatively, we have generated the first twelve digits of p (968 700 397 828) and q (895 124 411 025) based on I.
Their product is 867 107 373 065 471 689 253 700.
So far, things look good, and we have room for improvement...
And we are confident we can crack our current problem by April 30, 2021 in honor of the great Gauss (https://en.m.wikipedia.org/wiki/Carl_Friedrich_Gauss).
Relevant Reference Link:
https://www.wolframalpha.com/input/?i=968700397828*895124411025.
Guest wrote:Tentatively, we have generated the first twelve digits of p (968 700 397 828) and q (895 124 411 025) based on I.
Their product is 867 107 373 065 471 689 253 700.
So far, things look good, and we have room for improvement...
And we are confident we can crack our current problem by April 30, 2021 in honor of the great Gauss (https://en.m.wikipedia.org/wiki/Carl_Friedrich_Gauss).
...
Guest wrote:Updated Remark: We should be able to write a short program to gather data until a solution is found.
List of Possible Outcomes (data to be analyzed) for all [tex]1 \le i \le n[/tex]:
Data Table: [tex]( (p_{11 }, q_{11 }, \delta_{11} = I - p_{11 } * q_{11 }), (p_{12 }, q_{12 }, \delta_{12} = I - p_{12 } * q_{12 } ) ),
...,
( (p_{n1}, q_{n1 }, \delta_{n1} = I - p_{n1 } * q_{n1 }), (p_{n2 }, q_{n2 }, \delta_{i2} = I - p_{n2 } * q_{n2 }) )[/tex]
where [tex]\delta_{i1} > 0[/tex] and [tex]\delta_{i2} < 0[/tex].
We seek [tex]p_{ik }[/tex] and [tex]q_{ik }[/tex] such that [tex]\delta_{ik} = 0[/tex].
Guest wrote:Guest wrote:Updated Remark: We should be able to write a short program to gather data until a solution is found.
List of Possible Outcomes (data to be analyzed) for all [tex]1 \le i \le n[/tex]:
Data Table: [tex]( (p_{11 }, q_{11 }, \delta_{11} = I - p_{11 } * q_{11 }), (p_{12 }, q_{12 }, \delta_{12} = I - p_{12 } * q_{12 } ) ),
...,
( (p_{n1}, q_{n1 }, \delta_{n1} = I - p_{n1 } * q_{n1 }), (p_{n2 }, q_{n2 }, \delta_{n2} = I - p_{n2 } * q_{n2 }) )[/tex]
where [tex]\delta_{i1} > 0[/tex] and [tex]\delta_{i2} < 0[/tex].
We seek [tex]p_{ik }[/tex] and [tex]q_{ik }[/tex] such that [tex]\delta_{ik} = 0[/tex].
Guest wrote:Please post your correct answers, p and q, here. Otherwise, keep up the good work. And the results will come! Thank you!!
FYI: 'A Tour of Machine Learning Algorithms',
https://machinelearningmastery.com/a-tour-of-machine-learning-algorithms/.
Guest wrote:Important Remark:
[tex]8.7101... * 10^{499} \le q \le 9.311820446... * 10^{499}[/tex].
That helpful range makes our integer factorization problem a quite difficult problem!
Guest wrote:Guest wrote:Important Remark:
[tex]8.7101... * 10^{499} \le q \le 9.311820446... * 10^{499}[/tex].
That helpful range makes our integer factorization problem a quite difficult problem!
Remark: Our proposed range is approximate.
Guest wrote:Here's more homework!
[tex]q = \frac{-\delta + \sqrt{\delta^{2} + 4 * I}}{2}[/tex]
where [tex]\delta[/tex] is a positive even integer such that
[tex]2 \le \delta < 6.018 * 10^{498}[/tex].
Please select the correct [tex]\delta[/tex] to solve q.
Remark: There are almost [tex]3.09 * 10^{498}[/tex] choices for [tex]\delta[/tex].
Only one is correct.
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