This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(1)=711131719 because 711131719 is prime and the concatenation of 7, 11, 13, 17 and 19.
P:= select(isprime,[2,seq(p,p=3..10^4,2)]): select(isprime,[seq(P[i+3]+10^(1+ilog10(P[i+3]))*P[i+2] + 10^(2+ilog10(P[i+3])+ilog10(P[i+2]))*P[i+1] + 10^(3+ilog10(P[i+3])+ilog10(P[i+2])+ilog10(P[i+1]))*P[i], i=1..nops(P)-3)]); # Robert Israel, Apr 14 2016
The prime 113127131137139149 is a concatenation of the consecutive primes 113, 127, 131, 137, 139 and 149.
select(isprime, [seq(parse(cat([seq(ithprime(i), i=n+0..n+5)][])), n=1..500)])[]; # K. D. Bajpai, Mar 24 2014
Select[FromDigits[Flatten[IntegerDigits/@#]]&/@Partition[Prime[Range[ 300]],6,1],PrimeQ] (* Harvey P. Dale, Apr 30 2020 *)
172331 is a prime and appears in the sequence because it is the concatenation of prime(7), prime(7+2) and prime(7+4). 233141 is a prime and appears in the sequence because it is the concatenation of prime(9), prime(9+2) and prime(9+4).
with(StringTools): KD := proc() local a,b,d,e; a:=ithprime(n); b:=ithprime(n+2); d:=ithprime(n+4); e:= parse(cat(a,b,d)); if isprime(e) then RETURN (e); fi; end: seq(KD(), n=1..500);
Select[Table[FromDigits[Flatten[{IntegerDigits[Prime[n]], IntegerDigits[Prime[n+2]], IntegerDigits[Prime[n+4]]}]], {n,1,500}],PrimeQ]
1373 is a prime and appears in the sequence because it is the concatenation of prime(2+4), prime(2+2) and prime(2). 433729 is a prime and appears in the sequence because it is the concatenation of prime(10+4), prime(10+2) and prime(10).
with(StringTools): KD := proc() local a, b, d, e; a:=ithprime(n+4); b:=ithprime(n+2); d:=ithprime(n); e:= parse(cat(a, b, d)); if isprime(e) then RETURN (e); fi; end: seq(KD(), n=1..500);
Select[Table[FromDigits[Flatten[{IntegerDigits[Prime[n+4]],IntegerDigits[Prime[n+2]], IntegerDigits[Prime[n]]}]], {n,1,500}], PrimeQ]
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