A289867 Primes obtained from other primes by prefixing a 6.

67, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 683, 6101, 6113, 6131, 6151, 6163, 6173, 6197, 6199, 6211, 6229, 6257, 6263, 6269, 6271, 6277, 6311, 6317, 6337, 6353, 6359, 6367, 6373, 6379, 6389, 6397, 6421, 6449, 6491, 6521, 6547, 6563

Offset: 1

Author

Vincenzo Librandi, Jul 15 2017

Keywords

• nonn
• base

Examples

			613 is a term because it is a prime obtained by prefixing a 6 to the prime 13.
6101 is a term because it is a prime obtained by prefixing a 6 to the prime 101.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. similar sequences listed in A289866.

Programs

Magma

[k: p in PrimesUpTo(800) | IsPrime(k) where k is Seqint(Intseq(p) cat [6])];

Maple

p:= 0: A:= NULL:
while p < 1000 do
  p:= nextprime(p);
  q:= 10^(ilog10(p)+1)*6+p;
  if isprime(q) then A:= A, q; fi
od:
A; # Robert Israel, Jul 17 2017

Mathematica

Select[Table[FromDigits[Join[IntegerDigits[6], IntegerDigits[Prime[n]]]], {n, 110}], PrimeQ]
Select[6*10^IntegerLength[#]+#&/@Prime[Range[150]],PrimeQ] (* Harvey P. Dale, Apr 03 2022 *)

PARI

terms(n) = my(i=0); forprime(p=1, , my(s=eval(Str(6, p))); if(ispseudoprime(s), print1(s, ", "); i++); if(i==n, break))
/* Print initial 50 terms as follows */
terms(50) \\ Felix Fröhlich, Jul 15 2017