I found a condition for p, q that N=pq can be factored in plynominal time using Maple 2020.
Is fllowing Hypothesis and Proof is right?
N=pq p and q are large prime respectively.
R=q/p q > p R is very close to an small integer or a simple rational number.
N=pq can be factorized in time polynomial
point[p, q] is on y=N/x
y=N/x and y=Rx cross at point[p, q]
N is n digit
upper 2 digits N2 round off the 3rd digit
upper 3 digits N3 round off the 4th digit
upper 4 digits N4 round off the 5th digit
y=N2/x and y=Rx cross at point[p2,q2]
y=N3/x and y=Rx cross at point[p3,q3]
y=N4/x and y=Rx cross at point[p4, p4]
But we only know N.
Let line up candidates point[p2,q2] , point[p3,q3] and point[p4, p4]
N2 < 99 i=1..10 j=1..10
f2=N2/R2 - j^2
N4 < 9999 i=1..99 j=1.. sqrt(N4)
f4=N4/R4 - j^2
Point[j, i] that have small f2 and dn2 can be nominated as candidate for point[p2, q2]
Point[j, i] that have small f3 and dn3 can be nominated as candidate for point[p3, q3]
Point[j, i] that have small f4 and dn4 can be nominated as candidate for point[p4, q4]
Find cross point[px, qx] of y=R2x and y=N/x , y=R3x, y=N/x and y=R4x, y=N/x
Find the nearest prime pn for px and the nearest prime qn for qx
Number of candidates are finit.
You can factorized N=pq in time polynomial.
In addition, using "https://www.mapleprimes.com/questions/228532-Strange-Factorization"
Rang from p - half digits of p to p + half degits of p and /or range q - half digits of q to q + half degits of q N=pq can be factored in plynominal time.