I need to write a Program to factorise large dual-prime composite numbers of the form 'PQ' This little beauty for instance.

1881988129206079638386972394616504398071635633794173

8270076335642298885971523466548531906060650474304531

7388011303396716199692321205734031879550656996221305

168759307650257059

We note that there is a deterministic asymptotic series of cardinal number ratios that approximate closer and closer to the ratio of the two 'prime' factors of the above composite.

16/19.....405/481...437/519......2590/3076......2574/3057.....etc.

incidentally, (2574 - 144 = 6 x 405) more on that later.

The intention of the program is to test for 'squareness' the product of the small asymptotic ratios i.e. 405 x 481 = 174,805 and 174,805 x 1881988129206079...etc. is more pseudo-square than if multiplied by 16 x19 or 304,

It is rather a fun challenge, and as the numbers get larger, really quite difficult. but I am reasonably confident a simple program could factorise fairly large composites. I could write one in Fortran, my question is; could that translate into a modern program language, and which one would be best?

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