A099071 Composite numbers k such that the concatenation of all nonprime positive integers up to k in decreasing order is prime.

4, 6, 8, 9, 26, 1752

Offset: 1

Author

Farideh Firoozbakht, Nov 06 2004

Keywords

• base
• more
• nonn
• nice

Comments

The terms of this sequence are composite terms of the sequence A099070 with the same order. Next term is greater than 6000 and the prime corresponding to the next term has more than 20000 digits. Number of digits of primes corresponding to the six known terms of the sequence are respectively 2, 3, 4, 5, 29, and 5010.

Examples

			26 is a term: 26 is composite; nonprimes up to 26 are 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26; and 26252422212018161514121098641 is prime.
		

Links

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

Crossrefs

Cf. A099070, A100003, A046284.

Programs

Mathematica

Do[If[ !PrimeQ[n]&&PrimeQ[(v={};Do[If[ !PrimeQ[n+1-j], v=Join[v, IntegerDigits[n+1-j]]], {j, n}];FromDigits[v])], Print[n]], {n, 6013}]
cnpQ[n_]:=PrimeQ[FromDigits[Flatten[IntegerDigits/@Select[Range[n,1,-1],!PrimeQ[#]&]]]]; Select[Range[1800],!PrimeQ[#]&&cnpQ[#]&] (* Harvey P. Dale, Jul 19 2020 *)