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apocalyptic numbers
A number of the form    is called apocalyptic if its digits contain "666" as a substring.

The smallest apocalyptic number is  , which is equal to

while   is the smallest apocalyptic number which contains two 666 groups, being equal to
1684996666696914987166688442938726917102321526408785780068975640576.
The smallest power of 2 with 3 groups is  .

A number    such that    is apocalyptic is called apocalyptic power or apocalyptic exponent.

Between 1 and    there are 3715 numbers which are non-apocalyptic exponents, the largest being 29784. In other words, it is highly probable that    for    is an apocalyptic number.

Probably there are only 8 numbers, namely 2666, 3666, 5666, 6660, 6665, 6669, 11666, 26667 which contains 666 among their digits but are not apocalyptic exponents.

The first apocalyptic exponents are 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 more terms

The smallest 3 × 3 magic square made of consecutive apocalyptic numbers is

 1490 1478 1487 1482 1485 1488 1483 1492 1480

Below, the spiral pattern of apocalyptic numbers up to  . See the page on prime numbers for an explanation and links to similar pictures.

Apocalyptic exponents up to 30000 can also be... (you may click on names or numbers and on + to get more values)