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Palindromic beastly primes that begin and end with digit '1'.
1

%I #19 Sep 08 2022 08:46:13

%S 16661,1000000000000066600000000000001,

%T 10000000000000000000000000000000000000000006660000000000000000000000000000000000000000001

%N Palindromic beastly primes that begin and end with digit '1'.

%C The next term a(4) contains 1017 digits, and is too large to include in data section.

%H Tony Padilla and Brady Haran, <a href="https://www.youtube.com/watch?v=zk_Q9y_LNzg">The Most Evil Number</a>, Numberphile video (2018)

%e a(1) = 16661 is a palindromic prime that contains the beastly number '666' and begins and ends with digit 1.

%e a(2) = 1000000000000066600000000000001 is palindromic prime that contains the beastly number '666' and begins and ends with digit 1.

%p A260312:= n-> ((1*10^(n + 2) + 666)*10^n + 1 ): select(isprime, [seq((A260312 (n), n=1..100))]);

%t Select[Table[(1*10^(n + 2) + 666)*10^n + 1, {n, 1000}], PrimeQ]

%t Select[Table[FromDigits[Join[{1},PadRight[{},n,0],{6,6,6},PadRight[ {},n,0],{1}]],{n,0,50}],PrimeQ] (* _Harvey P. Dale_, Jul 09 2017 *)

%o (PARI) for(n=1, 500, k=((1*10^(n + 2) + 666)*10^n + 1 ); if(isprime(k), print1(k, ", ")));

%o (Magma) [k: n in [1..1000] | IsPrime(k) where k is ((1*10^(n + 2) + 666)*10^n + 1 )];

%Y Cf. A046720, A051003, A131645, A186086.

%K nonn,base,less

%O 1,1

%A _K. D. Bajpai_, Jul 22 2015