A097970 Numbers n such that 7*10^n + 3 is prime.

1, 4, 6, 16, 22, 39, 103, 163, 240, 1048, 1974, 2559, 5880, 14436, 28338, 32796, 38079, 56779, 91215, 111325, 115863, 138604

Offset: 1

Author

Julien Peter Benney (jpbenney(AT)ftml.net), Sep 07 2004

Keywords

• more
• nonn

Comments

a(23) > 2*10^5. - Robert Price, Aug 15 2015

Examples

			For n = 1 we have 7*10^1+3 =7*10+3 = 73, which is prime.
		

Links

• Makoto Kamada, Prime numbers of the form 700...003.
• Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.
• Index entries for primes involving repunits.

Crossrefs

Cf. A101129.

Programs

Magma

[n: n in [0..500] | IsPrime(7*10^n + 3)]; // Vincenzo Librandi, Aug 16 2015

Mathematica

Do[ If[ PrimeQ[ 7*10^n + 3], Print[ n ]], {n, 0, 10000}] (* Robert G. Wilson v, Jan 19 2005 *)
Flatten[Position[Table[7 10^n+3,{n,100000}],?PrimeQ]] (* _Harvey P. Dale, Nov 01 2011 *)
Select[Range[15000], PrimeQ[7 10^# + 3] &] (* Vincenzo Librandi, Aug 16 2015 *)

PARI

main(m)=select(n->isprime(7*10^n + 3),vector(m,i,i)) \\ Anders Hellström, Aug 15 2015

Formula

a(n) = A101129(n) + 1.

Extensions

a(10)-a(13) from Robert G. Wilson v, Jan 19 2005

a(14)-a(19) from Kamada data by Robert Price, Dec 14 2010

a(20)-a(22) from Robert Price, Aug 15 2015