OFFSET
1,1
COMMENTS
a(6) > 29505444491. - Jud McCranie, Jul 08 2000
a(6) > 10^12. - Jon E. Schoenfield, Sep 11 2008
a(6), if it exists, is larger than 10^14. - Giovanni Resta, Jan 09 2014
Also primes p with property that p divides 1 plus the sum of all composites < p. - Vicente Izquierdo Gomez, Aug 05 2014
a(7) > 253814097223614463, - Paul W. Dyson, Sep 27 2022
REFERENCES
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 71, p. 25, Ellipses, Paris 2008.
Harry L. Nelson, Prime Sums, J. Rec. Math., 14 (1981), 205-206.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 129.
LINKS
H. L. Nelson, Letter to the Editor re: Prime Sums, J. Recreational Mathematics 14.3 (1981-2), 205. (Annotated scanned copy)
Carlos Rivera, Puzzle 18. Some special sums of consecutive primes, The Prime Puzzles and Problems Connection.
EXAMPLE
2 divides 2;
5 divides 2 + 3 + 5;
71 divides 2 + 3 + 5 + 7 + ... + 61 + 67 + 71; etc.
MATHEMATICA
sumOfPrimes = 0; Do[ sumOfPrimes += p; If[ Divisible[ sumOfPrimes, p], Print[p]], {p, Prime /@ Range[23000000]}] (* Jean-François Alcover, Oct 22 2012 *)
Transpose[Module[{nn=23000000, pr}, pr=Prime[Range[nn]]; Select[Thread[ {Accumulate[ pr], pr}], Divisible[#[[1]], #[[2]]]&]]][[2]] (* Harvey P. Dale, Feb 09 2013 *)
PROG
(PARI) s=0; forprime(p=2, 1e9, s+=p; if(s%p==0, print1(p", "))) \\ Charles R Greathouse IV, Jul 22 2013
CROSSREFS
KEYWORD
nonn,nice,hard,more
AUTHOR
EXTENSIONS
Example corrected by Harvey P. Dale, Feb 09 2013
a(6) from Paul W. Dyson, Apr 16 2022
STATUS
approved