1 - First factor [6^101 + 10^101]
2 - You should get:
2^104 × 2 217557 × 265 896803 424061 × 1568 372427 881573 587879 × 5331 425490 815171 853272 879027
3 - Multiply 2^104 =20,282,409,603,651,670,423,947,251,286,016
4 - Take the square root of the result in 3 above:
5 - You should get: 4,503,599,627,370,496 - This is the largest n. So that:
6 - 4,503,599,627,370,496^2 = Result in 3 above which is a factor of 6^101 + 10^101.