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A100003 Prime numbers p such that the concatenation of all odd primes up through p in decreasing order is prime. 6
3, 5, 17, 89, 383, 8831 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
LINKS
Carlos Rivera, Puzzle 8. Primes by Listing, The Prime Puzzles and Problems Connection.
EXAMPLE
17 is in the sequence because 17.13.11.7.5.3 is prime (dot between numbers means concatenation).
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 *)
CROSSREFS
The actual prime concatenations in A092448 and the original concatenations in A092447. - Dmitry Kamenetsky, Mar 02 2009
Sequence in context: A351718 A281627 A102846 * A283331 A114161 A361180
KEYWORD
base,more,nonn,nice
AUTHOR
Farideh Firoozbakht, Nov 06 2004
STATUS
approved

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Last modified February 29 21:35 EST 2024. Contains 370428 sequences. (Running on oeis4.)