A099073 Numbers k such that the concatenation of the first k-1 odd primes in decreasing order is prime.

2, 3, 7, 24, 76, 1100

Offset: 1

Author

Farideh Firoozbakht, Nov 06 2004

Keywords

• base
• more
• nonn
• nice

Comments

A100003(n) = prime(a(n)). Next term is greater than 4500 and the prime corresponding to the next term has more than 21000 digits. Number of digits of primes corresponding to the six known terms of the sequence are respectively 1, 2, 9, 43, 198, and 4202. There is no known prime formed by concatenation of the first k odd primes in increasing order for 1 < k < 2250.

a(7) > 20000. - Michael S. Branicky, Nov 25 2024

Examples

			7 is in the sequence because the first 6 odd primes are 3,5,7,11,13,17 and 17.13.11.7.5.3 is prime (dot between numbers means concatenation).
		

Links

• Carlos Rivera, Puzzle 8. Primes by Listing, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A046035, A099070, A099071.

Programs

Mathematica

Do[If[PrimeQ[(v={};Do[v=Join[v, IntegerDigits[Prime[n-j+1]]], {j, n-1}];FromDigits[v])], Print[n]], {n, 2, 4500}]
Select[Range[1100],PrimeQ[FromDigits[Flatten[IntegerDigits/@ Reverse[ Prime[ Range[ 2,#]]]]]]&] (* Harvey P. Dale, Nov 12 2017 *)