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A100003 Prime numbers n such that the concatenation of all odd primes up through n in decreasing order is prime. 6

%I

%S 3,5,17,89,383,8831

%N Prime numbers n such that the concatenation of all odd primes up through n in decreasing order is prime.

%C 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.

%C 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.

%C a(7) > prime(28800) = 335033. - _Giovanni Resta_, Apr 01 2013

%H C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_008.htm">Primes by Listing</a>.

%e 17 is in the sequence because 17.13.11.7.5.3 is prime (dot between numbers means concatenation).

%t Do[If[PrimeQ[(v={};Do[v=Join[v, IntegerDigits[Prime[n-j+1]]], {j, n-1}];FromDigits[v])], Print[Prime[n]]], {n, 2, 4413}]

%t 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 *)

%Y Cf. A046284, A099070, A099071, A099073.

%Y The actual prime concatenations in A092448 and the original concatenations in A092447. - _Dmitry Kamenetsky_, Mar 02 2009

%K base,more,nonn,nice

%O 1,1

%A _Farideh Firoozbakht_, Nov 06 2004

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Last modified September 26 11:10 EDT 2020. Contains 337357 sequences. (Running on oeis4.)