Factorize 99899 into prime factors using just a pen and paper.
Suppose you want to factorize 35. √35 is a little less than 6. So there might be (6a)(6+a) that equals 35. Or if not, maybe (7a)(7+a) or if not, maybe (8a)(8+a). (61)(6+1) = 5*7 = 35. Success.
Now try 99899 whose square root is a bit over 316.
Maybe (317a)*(317+a) or maybe (318a)*(318+a).
317^2  99899 = 590
318^2  99899 = 1225 which is a perfect square (35^2), bingo.
(31835)(318+35)
283 * 353
I haven't proved 283 and 353 are prime, however.

Posted by Larry
on 20240728 13:39:40 