Googology Wiki
Advertisement
Googology Wiki
Not to be confused with Apocalyptic number.

An apocalypse number is a number having 666 digits in its decimal expansion.[1] There exist 10666 - 10665 = 9 × 10665 apocalypse numbers.

The smallest apocalypse prime is 10665 + 123, while the smallest apocalypse prime containing the number 666 is 10665 + 166,657[2], and the largest apocalypse prime is 10666 − 1,157.[3][4]

There are nine powers of single-digit numbers which are also apocalypse numbers (namely, 22,210, 22,211, 22,212, 31,394, 31,395, 5952, 6855, 7787 and 7788).

There are four f2(n) numbers which are also apocalypse numbers (namely, f2(2,198), f2(2,199), f2(2,200) and f2(2,201)).

There are two apocalyptic numbers which are also apocalypse numbers (namely, 22,210 and 22,212).

The 3184th Fibonacci number (F3184 where F1=1, F2=1, Fn = Fn-1 + Fn-2) is an apocalypse number.[5] Its decimal expansion is:[6]

116724374081495541233435764579214184068974717443439437236331282736262082452385312960682327210312278880768244979876073455971975198631224699392309001139062569109651074019651076081705393206023798479391897000377475124471344025467950768706990550322971334370940093654442411815206857904041043400568568081194379503001967669356633792347218656896136583990327918167352721163581650359577686552293102708827224247109476382115427568268820040258504986113408773333220873616459116726497198698915791355883431385556958002121928147052087175206748936366171253380422058802655291403358145619514604279465357644672902811711540760126772561572867155746070260678592297917904248853892358861771163

Finally, 273273 is also an apocalypse number.

Sources[]

See also[]

Advertisement