A100003 Prime numbers p such that the concatenation of all odd primes up through p in decreasing order is prime.

3, 5, 17, 89, 383, 8831

Offset: 1

Author

Farideh Firoozbakht, Nov 06 2004

Keywords

• base
• more
• nonn
• nice

Comments

Next term is greater than 4400th prime 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 1, 2, 9, 43, 198, 4202.

We can see the prime corresponding to 383 (the 5th term of the sequence) in the page related to puzzle 8 of the website of Carlos Rivera.

a(7) > prime(28800) = 335033. - Giovanni Resta, Apr 01 2013

Examples

			17 is in the sequence because 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. A046284, A099070, A099071, A099073.

The actual prime concatenations in A092448 and the original concatenations in A092447. - Dmitry Kamenetsky, Mar 02 2009

Programs

Mathematica

Do[If[PrimeQ[(v={};Do[v=Join[v, IntegerDigits[Prime[n-j+1]]], {j, n-1}];FromDigits[v])], Print[Prime[n]]], {n, 2, 4413}]
Prime[#]&/@Select[Range[100],PrimeQ[FromDigits[Flatten[IntegerDigits/@ Prime[Range[#,2,-1]]]]]&] (* To generate a(6) increase the Range by 1000, but the program will run a long time. *) (* Harvey P. Dale, Nov 27 2015 *)