A049500 Smallest prime p such that p + 4^k is also prime for all k = 1, ..., n.

3, 3, 3, 7, 7, 37, 37, 163, 671353, 13243063, 5906322013, 12087247687, 1523351345443, 1523351345443, 23631302781703

Offset: 1

Author

Labos Elemer

Keywords

• nonn
• more

Comments

a(13) > 10^11. - Donovan Johnson, Dec 02 2009

All terms from a(4) satisfy p == 7 or 13 (mod 30); a(16) > 10^14. - Mikk Heidemaa, May 12 2025

Examples

			Prime 3 generates the {3,7,19,67} exponential prime-chain of length 4 if the start is also counted.
The smallest "exponential 11-chain" starts with 13243063 as follows: 13243063, 13243067, 13243079, 13243127, 13243319, 13244087, 13247159, 13259447, 13308599, 13505207, 14291639.
		

Crossrefs

Cf. A023200, A049492-A049499.

Programs

Mathematica

Table[p = 2; While[Times @@ Boole@ PrimeQ[p + 4^Range@ n] != 1, p = NextPrime@ p]; p, {n, 10}] (* Michael De Vlieger, Mar 05 2017 *)

PARI

okchain(n, p)=for (k=1, n, if (! isprime(p + 4^k), return (0));); return (1);
a(n) = {p = 2; while (! okchain(n, p), p = nextprime(p+1)); p;} \\ Michel Marcus, Dec 17 2013

Extensions

a(11)-a(12) from Donovan Johnson, Dec 02 2009

a(13)-a(15) from Mikk Heidemaa, May 12 2025