2^666 - The Exponentiation of the Beast!

MATHEMATICA giving us all exponentiations of 2 up until 1000, finding those with the string 666.

power2 = 2^# & /@ Range[0, 1000];
satanic = (! StringFreeQ[#, "666"]) & /@ (ToString /@ power2);
Pick[Range[0, 1000], satanic]

{157, 192, 218, 220, 222, 224, 226, 243, 245, 247, 251, 278, 285, \
286, 287, 312, 355, 361, 366, 382, 384, 390, 394, 411, 434, 443, 478, \
497, 499, 506, 508, 528, 529, 539, 540, 541, 564, 578, 580, 582, 583, \
610, 612, 614, 620, 624, 635, 646, 647, 648, 649, 650, 660, 662, 664, \
666, 667, 669, 671, 684, 686, 693, 700, 702, 704, 714, 718, 720, 723, \
747, 748, 749, 787, 800, 807, 819, 820, 822, 823, 824, 826, 828, 836, \
838, 840, 841, 842, 844, 846, 848, 850, 857, 859, 861, 864, 865, 866, \
867, 868, 869, 871, 873, 875, 882, 884, 894, 898, 920, 922, 924, 925, \
927, 928, 929, 931, 937, 970, 972, 975, 977, 979, 981, 983, 985, 994}

2^{^666}=
3061802069160839023092406500876024752826394864138->666<-225770884719135200\
2289478439035090073805055513810523453685782024507137361403148294216156\
5170086143298589738273508330367307539078392896587187265470464 

Thanks to Hauke Reddmann for the information and code above! I contacted him after seeing that 2^{^800} starts with "666".