A359406 Integers k such that the concatenation of k consecutive primes starting at 31 is prime.

1, 2, 3, 23, 43, 141

Offset: 1

Author

Mikk Heidemaa, Dec 30 2022

Keywords

• nonn
• base
• more

Comments

The corresponding primes (p) known (31, 3137, 313741, ...) have an even number of digits and p (mod 10) == 1|7. For those at a(1)...a(6), p (mod 3) == p (mod 5) holds.

a(7): 3472 corresponds to a 15968-digit probable prime (certification in progress).

For a(8), k > 15000 (if it exists).

a(8) > 30000. - Tyler Busby, Feb 13 2023

Examples

			2 is a term because the consecutive primes 31 and 37 concatenated to 3137 yield another prime.
		

Crossrefs

Cf. A069151, A309191, A030996, A280894.

Programs

Mathematica

UpToK[k_] := Block[{a := FromDigits @ Flatten @ IntegerDigits @ Join[{}, Prime @ Range[11, i]]}, Reap[ Do[ If[ PrimeQ[a], Sow[i - 10], Sow[Nothing]], {i, k}]]][[2, 1]]; UpToK[3500] (* or *)
UpToK[k_] := Flatten @ Parallelize @ MapIndexed[ If[ PrimeQ[#1], #2, Nothing] &, DeleteCases[ FromDigits /@ Flatten /@ IntegerDigits @ Prime @ Range[11, Range[k]], 0]]; UpToK[3500]