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2021-08-02, 08:41   #17
Alberico Lepore

May 2017
ITALY

23·5·13 Posts

Quote:
 Originally Posted by Alberico Lepore ********************************************************************* UPDATE: I tried to solve in x and I noticed that the first valid value is our x = 159757905 if it would always happen the cost of factoring 390644893234047643 would be 7454 * 10 = 74540 Tomorrow morning I will continue with other tests https://www.wolframalpha.com/input/?...%2F8+%2Ch+%2Cy
unfortunately this is not true.

But x is very close to min_range_x

I tested on a number of 30 digits with p and q of 15 digits and the result is 37

N=188723059539473758658629052963

N=188723059539473758658629052963
,
sqrt(N/(18/10))=a
,
(18/10*a+a-4)/8=x
,
2*x*(x+1)-b*(b-1)/2=(N-3)/8

b=64759908643727

h=x-(64759908643726)/2-88973930
,
[2*(h-1)*(h-1+1)]
<
(188723059539473758658629052963-3)/8-(64759908643726)/2*(4*x+1-2*(y-1))
<=
[2*h*(h+1)]
,
2*(x)*(x+1)-y*(y-1)/2=(188723059539473758658629052963-3)/8

range x 113364197263548<=x<=113364197263741

size_range 193

distance x 37

x=113364197263585

I need to be able to quantify distance x or size_range_x

total cost [10*my_quantify *88973930] about N ^ (1/3)

It's still a very heavy bruteforce, but I'm happy

Last fiddled with by Alberico Lepore on 2021-08-02 at 08:50 Reason: [10*my_quantify *88973930]