Start by factoring out the easy bits:
8888888899999999 = 11111111*800000009
The factoring program on my calculator can easily handle 5-digit numbers like 10001, but not 9-digit numbers. If I let it run long enough I can easily see 80000009 is either prime or has prime factors above 10001.
Turning to Wolfram|Alpha I can get the last factors (it feels like cheating) and 800000009=15299*52291.
So the largest prime factor is 52291.
And my calculator just found it as I was typing!
Posted by Jer
on 2019-03-19 10:06:22