8 6 , 2 3 1 , 5 9 0 , 7 7 2 , 9 3 1 ,..., 3 0 4 , 8 3 5 , 3 5 6 , 3 2 9 , 6 2 4 , 2 2 4 , 1 3 7 , 2 1 6 ▁ ▁The ▁maximum ▁number ▁that ▁can ▁fit ▁in ▁an ▁IE EE ▁double - prec ision ▁floating - point ▁format , ▁and ▁hence ▁the ▁maximum ▁number ▁that ▁can ▁be ▁represented ▁by ▁many ▁programs , ▁for ▁example ▁Microsoft ▁Excel . ▁▁ 2 8 2 , 5 8 9 , 9 3 3 ▁= ▁ 1 4 8 , 8 9 4 , 4 4 5 , 7 4 2 , 0 4 1 ,..., 2 1 0 , 3 2 5 , 2 1 7 , 9 0 2 , 5 9 2 ▁ ▁One ▁more ▁than ▁the ▁largest ▁known ▁prime ▁number ▁. ▁It ▁has ▁more ▁than ▁ 2 4 ▁million ▁digits . ▁ ▁Other ▁properties ▁The ▁sum ▁of ▁all ▁- choose ▁bin omial ▁coefficients ▁is ▁equal ▁to ▁. ▁Consider ▁the ▁set ▁of ▁all ▁- digit ▁binary ▁integers . ▁Its ▁cardinal ity ▁is ▁. ▁It ▁is ▁also ▁the ▁sums ▁of ▁the ▁cardinal ities ▁of ▁certain ▁subsets : ▁the ▁subset ▁of ▁integers ▁with ▁no ▁ 1 s ▁( cons isting ▁of ▁a ▁single ▁number , ▁written ▁as ▁▁ 0 s ), ▁the ▁subset ▁with ▁a ▁single ▁ 1 , ▁the ▁subset ▁with ▁two ▁ 1 s , ▁and ▁so ▁on ▁up ▁to ▁the ▁subset ▁with ▁▁